SIA-Smaart Schools & Applications Seminars

Transcription

1 SIA-Smaart Schools & Applications Seminars Presented by: SIA Software Company, Inc A LOUD Technologies, Inc. Company

2 Copyright 2004 SIA Software Company, Inc A LOUD Technologies Company One Main Street, Whitinsville, MA All rights reserved

3 SmaartLive Fundamentals and Applications: PowerPoint Notes Presented by: SIA Software Company, Inc A LOUD Technologies, Inc. Company

4 Copyright SIA Software Company, Inc. A LOUD Technologies, Inc. Company All rights reserved

5 SIA Smaart Schools & Applications Seminars SmaartLive Fundamentals PowerPoint: Class Notes This PowerPoint presentation can be downloaded at: Copyright SIA Software Company, Inc. A LOUD Technologies, Inc. Company All rights reserved Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 1

6 SIA Smaart Schools & Applications Seminars SIA Contact Info Jamie Anderson SIA Product Manager Calvert Dayton SIA Development Manager Barbara Stolakis SIA Office Manager Other SIA Addresses: SIA Software Company, Inc One Main Street Whitinsville, MA Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 2

7 SIA Smaart Schools & Applications Seminars FFT s Fast Fourier Transforms Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 3

8 SIA Smaart Schools & Applications Seminars Transforms A transform converts data from one domain/view to another: Time Domain to Frequency Domain Same data Is reversible via Inverse Transform Unlike a conventional RTA using a bank of analog filters, FFT s yield complex data: Magnitude and Phase data Time Domain Waveform Frequency Domain Spectrum* Amp vs Time Amp vs Freq (*Fractional Octave Banded View) What do you get if you transform a transfer function? Inverse Fourier Transform (IFT) of Frequency Response produces Impulse Response Transfer Function To Impulse Response Frequency Domain to Time Domain *So... If Frequency Response can be measured with music... so can Impulse Response* Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 4

9 SIA Smaart Schools & Applications Seminars FFT Resolution Reciprocal Bandwidth: FR=1/TC Frequency Resolution = 1/Time Constant Larger Time Window: Higher Resolution Slower (Longer time window and more data to crunch) Smaller Time Window: Lower Resolution Faster Time Constant = Sample Rate x FFT Length * Decimation Varying SR & FFT to get constant res.* The Only Math You Need Today: ƒ = 100 Hz T= 10 ms T=.1 ms ƒ = 10 khz ƒ = 500 Hz T= 2 ms T=1/ƒ & ƒ=1/t T= 1 ms ƒ = 1 khz ƒ = 20 Hz T= 50 ms ƒ = 250 Hz T= 4 ms T=.1 ms ƒ = 10 khz T=.5 ms ƒ = 2 khz Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 5

10 SIA Smaart Schools & Applications Seminars FFT Parameters: Time Constant (TC) vs. Frequency Resolution (FR) Linear Frequency Scale TC = FFT/SR FR = 1/TC FFT Parameters: Time Constant (TC) vs. Frequency Resolution (FR) Log Frequency Scale Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 6

11 SIA Smaart Schools & Applications Seminars Linear vs. Log Banding FFT s yield linear data Constant bandwidth instead of constant Q FFT data must be banded to yield fractional-octave data. Pink Noise (equal energy per octave) shown w/ linear and log banding. Linear banding has an increasing number of bands per octave as frequency increases, resulting in less energy per band in the HF. Fractional octave (log) banding has an equal number of bands per octave, resulting in equal energy per band. FPPO 24 Fixed Points Per Octave (Only available in Transfer Function Mode) TC = 3 ms TC = 683 ms FPPO mode utilizes multiple FFT s of varying TC to produce data that has a constant 24 th oct. resolution. Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 7

12 SIA Smaart Schools & Applications Seminars Transfer Function (Frequency Response) Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 8

13 SIA Smaart Schools & Applications Seminars Transfer Function Input Signal System Output Signal Measurement Channel (RTA) Reference Channel (RTA) Transfer Function Transfer Function Input Signal System Output Signal Measurement Channel (RTA) Reference Channel (RTA) Transfer Function Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 9

14 SIA Smaart Schools & Applications Seminars Transfer Function Input Signal System Output Signal Measurement Channel (RTA) Reference Channel (RTA) Transfer Function Dual-Channel Measurement Issues: Input Signal System Delay = x ms Output Signal Propagation Time Linearity - Does response change with level? Noise Averaging Coherence Ref Signal Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 10

15 SIA Smaart Schools & Applications Seminars Coherence Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 11

16 SIA Smaart Schools & Applications Seminars Coherence How stable/consistent is your data? Coherence indicates the linearity/quality of each data point in your transfer function measurement. Given as a value between 0 to 1 (0% - 100%) 100% = Highest Coherence = great data 0% = Lowest Coherence = bogus data Coherence Scale 100% (Top of Plot) 0% (Middle of Plot) Coherence Three causes of bad coherence: 1. Bad measurement Check measurement delay Check measurement signals Check measurement set-up Check equipment Look for broad ranges of bad coherence. Particularly in HF if Smaart s delay is set wrong. Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 12

17 SIA Smaart Schools & Applications Seminars Coherence Three causes of bad coherence: 1. Bad measurement 2. Poor Signal to Noise Ratio Turn up measurement level Turn down noise If due to external noise, coherence should improve with measurement SPL. At what SPL should I measure? How loud is loud enough? (For accurate measurements) Slowly turn up your measurement signal level... When the coherence trace no longer improves, you re there! Coherence Three causes of bad coherence: 1. Bad measurement 2. Poor Signal to Noise Ratio 3. Poor Direct to Reverb Ratio Move mic closer to source Move source closer to mic Damp reverberance Real World Coherence. It is common to get a bad Coh spike where you see a cancellation, Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 13

18 SIA Smaart Schools & Applications Seminars How Smaart Works Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 14

19 SIA Smaart Schools & Applications Seminars How Smaart Works Input System Output FFT Spectrum Views FFT RTA Wave Spectrum Spectrograph SPL History How Smaart Works Input System Output FFT FFT = Transfer Function (Frequency Resp.) Wave Spectrum Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 15

20 SIA Smaart Schools & Applications Seminars How Smaart Works Input System Output FFT FFT = Transfer Function (Frequency Resp.) IFT Impulse Resp. Wave Spectrum Basic Measurement Set-up Source EQ / Processor Amplifier Loudspeaker & Room Microphone Computer w/ Stereo line-level input Mixer: Signal Selector & Pre-amps Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 16

21 SIA Smaart Schools & Applications Seminars Mode by Mode: Configuration Notes Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 17

22 SIA Smaart Schools & Applications Seminars Class Notes Getting Started Point Smaart at your stereo input device Set as Wave Input in Options:Devices Set bit depth (Use 16 bit as default unless you know otherwise) Use [Alt + V ] to display the Windows Record In Panel Hit Start to begin processing inputs Verify that signals are getting to Smaart Ref. on Right (Blue) channel Meas. on Left (Green) channel Optimum signal input level is ~ -12dB Right where meters turn yellow Leaves enough headroom for dynamic signals Class Notes Spectrum Mode FFT Parameter Set and Forgets Three goals for an RTA 1. Resolution 2. Responsiveness 3. Correlation to human hearing FFT Size Larger FFT s provide higher freq resolution Smaller FFT s have faster response and easier to process Find the right trade off of resolution v. response (try 16k) Sample Rate (SR) SR determines highest measurable freq = ½ SR = Nyquist SR determines time resolution = 1 sample =.02 ms at 48k Use highest SR for your default setting (48k) Use Fractional-Octave Banding (Oct, 1/3, 1/6, 1/12, 1/24) Fractional octave banding provides best correlation to human hearing Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 18

23 SIA Smaart Schools & Applications Seminars Class Notes Spectrum Mode: SPL Calibration 1. View 1/3 octave scale 2. Use calibrator to generate tone of known SPL at mic. 3. Double-click anywhere in the RTA plot area 4. Type calibrator SPL into Set this value to db Remember: Smaart s SPL calibration is dependent upon mic sensitivity and input pre-amp gain. See your Quick Reference Card for alternative methods of SPL calibration IFYOU CHANGE EITHER YOU MUST RECALIBRATE Class Notes Remember to set your delay! Transfer Function Mode Recommended Settings Input Meters: Optimum input level -12 Where the meter turns yellow Coherence Threshold: 10% - 15% Just enough to remove the truly bogus data Averages: Acoustic Measurements: 64(+) Electronic Measurements: 8-16 More averages = better s/n & trace stability Magnitude Threshold: 16 bit Input Device: 35% 24 bit Input Device: 55% FFT Parameters: Acoustic Measurements: FFT = FPPO Electronic Measurements: FFT = 16k or 32k Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 19

24 SIA Smaart Schools & Applications Seminars Class Notes Impulse Response Three ways to improve the dynamic range of your impulse response measurement: 1. Measure louder Improve true s/n 2. Increase Averages Each doubling of Avgs gives 3 db better s/n 3. Increase TC/FFT Size Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 20

25 SIA Smaart Schools & Applications Seminars System Alignment Notes Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 21

26 SIA Smaart Schools & Applications Seminars Tools in Order of Use 1 Acoustic Design / Treatment Equipment Choice / Maintenance System Design - Design to align 2 Level Delay 3 And lastly... EQ System Engineering Key Concepts: Systems interact most where they are equal level. Phase/Time determines how they will interact. Solve the problem at the source. Use the right tool. Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 22

27 SIA Smaart Schools & Applications Seminars Comb Filters & Sine Wave Addition Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 23

28 SIA Smaart Schools & Applications Seminars Addition of Sine Waves of Same Frequency and Equal Amplitude ²ø = 0 Complete Addition ²ø = 90 Partial Addition ²ø = 120 No Addition ²ø = 180 Complete Cancellation ²ø = 240 No Addition Period and Frequency T = 4 ms ƒ = 1/4 ms = 250 Hz O ms 1 ms 2 ms 3 ms 4 ms T = 3 ms ƒ = 1/3 ms = 333 Hz O ms 1 ms 2 ms 3 ms 4 ms T = 2 ms ƒ = 1/2 ms = 500 Hz O ms 1 ms 2 ms 3 ms 4 ms T = 1.5 ms ƒ = 1/1.5 ms = 666 Hz O ms 1 ms 2 ms 3 ms 4 ms T = 1 ms ƒ = 1/1 ms = 1000 Hz O ms 1 ms 2 ms 3 ms 4 ms T =.5 ms ƒ = 1/.5 ms = 2000 Hz Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 24

29 SIA Smaart Schools & Applications Seminars Phase Shift vs. Frequency: Group Delay = 1 ms 1 ms ƒ = 250 Hz ²ø = 90 O ms 1 ms 2 ms 3 ms 4 ms ƒ = 333 Hz ²ø = 120 O ms 1 ms 2 ms 3 ms 4 ms ƒ = 500 Hz ²ø = 180 O ms 1 ms 2 ms 3 ms 4 ms ƒ = 666 Hz ²ø = 240 O ms 1 ms 2 ms 3 ms 4 ms ƒ = 1000 Hz ²ø = 360 O ms 1 ms 2 ms 3 ms 4 ms ƒ = 2000 Hz ²ø = 720 The Ground Bounce Reflection arrives ~ 4 ms 4 ms Comb filter frequency = 1 / 4 ms = 250 Hz Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 25

30 SIA Smaart Schools & Applications Seminars Reflection Arrival vs. Comb Freq. 1 ms 1 khz 2 ms 500 Hz 4 ms 250 Hz 10 ms 100 Hz The Ground Bounce Two Solutions Block the reflection Remember: Baffle must be large enough to be effective above 100 Hz. Think 5 x 5 (1.5 m x 1.5 m) Ground-plane measurement Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 26

31 SIA Smaart Schools & Applications Seminars Reading Delay in the Phase Trace Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 27

32 SIA Smaart Schools & Applications Seminars Smaart Measurement Delay Time Input System Delay Smaart Delay Measurement Signal Reference Signal Phase Trace Angle Shows Delay Time Phase Trace Angle System Meas Smaart Ref Measurement Signal Lags Reference Signal Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 28

33 SIA Smaart Schools & Applications Seminars Phase Trace Angle Shows Delay Time Phase Trace Angle System Meas Smaart Ref Measurement Signal Aligned to Reference Phase Trace Angle Shows Delay Time Phase Trace Angle System Meas Smaart Ref Measurement Signal Leads Reference Signal Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 29

34 SIA Smaart Schools & Applications Seminars Notes Copyright 2004 SIA Software Company Inc. - a LOUD Technologies Company One Main St Whitinsville, MA ph fax 30

35 SIA-Smaart Application Notes Getting Started with SmaartLive: Basic Measurement Setup and Procedures Presented by: SIA Software Company, Inc A LOUD Technologies, Inc. Company

36 Copyright SIA Software Company, Inc. A LOUD Technologies, Inc. Company All rights reserved

37 Getting Started with SmaartLive: Basic Measurement Setup and Procedures Paul D. Henderson This document serves as a starting point for learning to use SIA SmaartLive for basic measurements of audio systems and components. Here, we will discuss the capabilities of SmaartLive and the basic measurement hardware necessary to perform successful measurements. A series of tutorial examples will be presented, which will serve as a hands-on introduction to making measurements with the system. I. The Primary Measurement Functions of SmaartLive Fundamentally, SmaartLive is a software-based dual-channel audio analyzer, capable of performing a large number of measurement tasks required by the audio professional. While SmaartLive is not intended to replace critical listening and human experience, the intelligent application of the measurement platform to the task of configuring, troubleshooting, and optimizing systems provides the user with significant advantages. Table 1 outlines the basic measurement modes of SmaartLive, with a synopsis of some of the common uses and capabilities for each. SmaartLive Mode Primary Capabilities Applications Spectrum Transfer function Impulse Real-time spectrum analysis Narrowband and fractional-octave display Calibration to real-world sound pressure level with SPL metering Running SPL log and spectrograph functions Real-time transfer function analysis Configurable magnitude and phase display Narrowband and Fixed-Point-per-Octave analysis Real-time coherence display Impulse response measurement Linear, log, and ETC display Automatic estimates of propagation delay times Table 1: Basic measurement modes in SmaartLive. Live source spectrum monitoring SPL monitoring for live performance Noise level analysis Feedback detection Transfer function measurements of loudspeakers, equalizers, sound systems Real-time optimization of systems (incl. equalizers, crossovers, delays, etc.) Measurement of sound system / room impulse response Configuration of loudspeaker delays, etc. In addition to the capabilities in Table 1, SmaartLive contains an internal signal generator that simplifies the measurement process by creating the appropriate excitation signals for each measurement. This eliminates the need for an external device dedicated to producing measurement signals for use with SmaartLive. SmaartLive also includes significant capabilities for controlling external devices, such as loudspeaker processors, equalizers, etc. This useful functionality will not, however, be discussed in this document. SIA Software Company, Inc. is not responsible for damage to your equipment resulting from improper use of this product. Be sure that you understand and observe the proper input and output levels, impedances and wiring conventions of all system components before attempting the measurements described in this document. Getting Started with SmaartLive: Basic Measurement Setup and Procedures Page 1

38 II. Components of a Basic SmaartLive Setup To use SmaartLive effectively, you should have on hand a basic set of measurement equipment. The list below outlines the fundamental components of a SmaartLive measurement setup. Details regarding the connection of your equipment for specific measurement tasks will be presented in later sections. Component Measurement Microphone Guidelines If you intend to measure anything beyond simple electronic devices, you will need a measurement microphone to acquire acoustical signals. The basic job of the microphone is to convert acoustical pressure at a point into a voltage as accurately as possible, so your microphone should be omnidirectional with a flat frequency response. Most commercially available measurement microphones are based on an electret condenser design, which will require some form of power, either through phantom power from your preamplifier or by an internal battery. You may also desire a microphone calibrator to accurately perform calibrated sound pressure measurements. Microphone Preamplifier To interface with your microphone, you will typically need some form of microphone preamplifier. The preamplifier should possess a low noise floor and sufficient gain for reasonable use. For most measurement microphones, the preamplifier should include phantom power to power the microphone. Note that many users may prefer to use a small mixer, routing device, or even a front-of-house console in place of a dedicated preamplifier. In these cases, make sure to disable all channel processing before use (equalization, dynamics processing, etc.). Sound Card For full functionality, SmaartLive requires a compatible sound card with at least two independent line-level input channels (usually in the form of a single stereo input) and a line-level output. Some notebook computers with built-in sound capabilities only offer a single channel (mono) input, so make certain your system meets this criterion. Without a stereo input, you will be unable to utilize the transfer function and impulse measurement capabilities. Note that external hardware solutions are available, some of which combine highquality A/D and D/A converters with built-in microphone preamplifiers. These may prove to be maximally convenient for field use, are readily available with USB, PCMCIA, and Firewire interfaces. Regardless of the input device you select, it must use a Windows -compatible Wave audio device driver. Other device driver types, including ASIO, are note currently supported by SmaartLive. Computer with SIA-SmaartLive The computer should adhere to at least the minimum requirements for running SmaartLive, which are available in the SmaartLive User Guide or by accessing the SIA Software website at For portable field operation, a notebook computer is most convenient. Cabling and Interconnections You should have on hand the appropriate cables for connecting your measurement system and interfacing with the equipment that you are measuring. Use only professional-quality cables, avoiding inferior adapters and consumer-grade interconnections. If your computer sound card uses 3-conductor 1/8-inch stereo phone connectors for interface, you may obtain breakout cables that allow you to convert this interface to 1/4-inch phone or XLR connectors. Getting Started with SmaartLive: Basic Measurement Setup and Procedures Page 2

39 III. Getting Signals into SmaartLive Now that you have assembled the equipment necessary to operate SmaartLive, we will discuss the process of setting up the system to recognize your hardware and adjusting the signal levels through the system. Make sure your sound card is online (if external, connect it) and start SmaartLive. If you are using an external audio device, do not disconnect it while SmaartLive is running. To select the proper sound card for use by the system, click Options? Devices on the menu, or press Alt+A. The window in Figure 1 will appear. Select your sound card input device in the Wave In drop-down box, and do the same for the output device in the Wave Out box. If your device supports input or output resolution higher than 16 bits, select the appropriate values in the Bits Per Sample boxes. Now, you may connect devices to the outputs and inputs of your soundcard, and the signals will be correctly handled by SmaartLive. Figure 1: Select your sound card as the input and output device. Many soundcards use internal mixing circuitry to mix many audio streams together to the master output, or to select and/or mix the signals together that will be seen by the sound card inputs. You may need to configure these options for your card to enable the line-level input and also to enable the wave output. These options may be set by launching the Windows mixer application, seen in Figure 2. You may launch the mixer by pressing Alt+V on the keyboard in SmaartLive. See the SmaartLive User Guide for more detailed information. (a) (b) A note about levels: the signal generator level is controlled by the level setting spinner on the generator, which defaults to a Figure 2: Configure the input (a) and output (b) mixers for your device if necessary. low level to prevent equipment damage at first use. This, in combination with output levels and mixer settings for your device, varies the signal level seen at the sound card output. For most measurements where the signal generator is required, you will desire to adjust the overall generator level to a high enough level to avoid noise in the measurement, but not so high a level as to cause damage or discomfort. The input levels, however, must be carefully adjusted to eliminate signal clipping on the sound card A/D converters while maintaining a high enough signal level to minimize extraneous noise. At any time SmaartLive is running, the input level meters in Figure 3 are active, which indicate the peak input levels seen by the A/D converters in the sound card. If the levels are too low (Figure 3a), noise from the sound card and other analog devices may compromise the measurement. If the levels are two high, the clipping indicators will light (Figure 3c), and you must reduce the input level to perform meaningful measurements. For most measurements, maintain a nominal input level between -12 and -6 db. (a) (b) (c) Figure 3: Make sure input levels are neither too low (a) nor too high (c). Input levels should usually be around -12 to -6 db for basic measurements (b). Getting Started with SmaartLive: Basic Measurement Setup and Procedures Page 3

40 IV. Measurement Examples Now, we will explore some examples of basic measurements using SmaartLive. The following pages will introduce you to the fundamentals of making Spectrum (RTA), Transfer Function, and Impulse Response measurements. The examples presented here are arranged in order of complexity; the later examples build on concepts presented in preceding sections. We recommend that you proceed through these exercises in order. Each example will present the basic hardware configuration, as well as sample measurement results. Keep in mind that your data may appear different than the data presented here; the sample results are simply representative of what you might see. Example Application 1 SmaartLive as a Real-Time Spectrum Analyzer (RTA) The most basic functionality of SmaartLive lies in its Spectrum mode, which enables two channels of real-time spectrum analysis. In this mode, SmaartLive contains functions similar to a hardware RTA (real-time analyzer), where the incoming signals are decomposed into frequency components and displayed dynamically. By default, SmaartLive displays the two channels as a real-time bar graph of energy vs. frequency, with each bar representing a band of energy 1/12 th -octave wide, although many other displays are possible. Connecting the System To make use of this mode, connect any compatible audio signal to at least one input of your sound card. In RTA mode, you may monitor two channels simultaneously, so you could connect a measurement microphone to one channel and the output of a mixing console to the other, among other possibilities. Measurement Microphone Microphone Preamplifier Line Input L R Computer with SmaartLive TM Mixing Console Figure 4: Example hardware configuration for RTA measurement. Figure 4 shows the hardware configuration for this example. Any line-level signal may be used as an input source, although it is somewhat educational to perform this introductory measurement with a live microphone connected through a preamplifier. Now, launch SmaartLive, which should default into Spectrum mode. At any time, you may change the current measurement mode by clicking one of the mode buttons. Press the ON button to begin the real-time measurement. Measurement mode buttons Getting Started with SmaartLive: Basic Measurement Setup and Procedures Page 4

41 You should now see a live banded spectrum of the input signals as in Figure 5 (both channels are visible by default). If you are using a live microphone, the spectrum display will respond to any noise in the room, and whistling near the microphone will drive the bands noticeably upward near the frequency of your whistle. You may experiment with different views of the incoming data by selecting a different data scale with the Scale spinner; data may be presented in 1/1, 1/3, 1/6, 1/12, and 1/24-octave Figure 5: Default live RTA spectrum display (1/12 th -octave). bands or as a narrowband power spectrum on either a logarithmic or linear frequency axis. Also configurable are the basic Fast Fourier Transform (FFT) parameters, averaging, and weighting. Averaging may be used to vary the time behavior of the spectrum display, allowing you to look at either the instantaneous behavior of the signal or its long-term spectral content. Averaging may be configured with various options, including Slow, Fast, and Exp, which represent exponentially decaying behavior, Inf, which maintains an evenly-weighted average of all data since initialization, and numeric values between 1 and 128, which evenly weight the last n measurements. You may reseed the averaging buffers at any time by pressing V on the keyboard. The spectrum mode contains many other useful features, including absolute calibration, integrated SPL metering and logging, and real-time spectrogram functions (Figure 6). Note that these functions will display data for the active input channel only. The active channel may be assigned by clicking on the associated input level meter. Please see the included documentation for more information on the use of these more advanced functions. SmaartLive s Spectrum mode displays are very useful for identifying feedback frequencies, looking at room noise, studying the spectral content of musical material, and has many other uses. Historically, many have employed RTA methods for measuring the frequency response of a system and performing equalization; we do not recommend using this technique, as the transfer function measurement capability of SmaartLive is a far more useful and accurate tool for this task. The Spectrum mode is inherently unable to distinguish direct sound from reflective energy and to discriminate between the excitation signal and uncorrelated noise, which limits its usefulness in sound system response optimization tasks. (a) (b) (c) Figure 6: Sample advanced Spectrum-mode measurements; (a) Spectrograph, (b) SPL time history, (c) Real-time calibrated SPL. Getting Started with SmaartLive: Basic Measurement Setup and Procedures Page 5

42 Example Application 2 Measuring an Analog Equalizer In this example, we will introduce the use of SmaartLive s real-time Transfer Function measurement capability to measure the frequency response of an analog equalizer. To perform this exercise, you will need an equalizer, crossover, or some other filtering signal processor. An analog device is best for this example; digital devices include some throughput delay from input to output that must be found and compensated for, using SmaartLive s internal signal delay (we will discuss this in subsequent examples). Out Equalizer In Line Input L R Computer with SmaartLive TM Line Output L R -or- Figure 7: Hardware configuration for measuring an equalizer. Connecting the System Connect the system as shown in Figure 7, with the sound card output driving both the input of the equalizer and the right input of the sound card (called the reference input). The output of the equalizer is brought into the computer through the left input (called the measurement input). The internal signal generator in SmaartLive will be used to excite the equalizer and measure its response. By using this connection scheme, SmaartLive compares the exact representation of the generator output to the returning signal from the equalizer, effectively canceling any imperfections introduced by the sound card. Adjusting Signal Levels Start the SmaartLive generator by clicking the GEN (Generator On) button; the system will now begin generating random pink noise that will appear on the sound card output. The generator defaults to a low level (-36 db), so use the generator level spinner to increase the output to a reasonable level. The level should be high enough that the dynamic range of the system and equalizer is adequately utilized; try for a generator level of around -6 db, as a rule of thumb target, to optimize the performance of the internal generator. If the analyzer is not running, click the ON button to start it. Now, adjust the input controls to bring the input signal to a reasonable level (as in Figure 3). If the equalizer is bypassed or its controls set to 0 db, the transfer function display should be an approximately flat line. If not, it is likely that there is some gain error in the system or the device itself contains some gain or attenuation factor. You may adjust the measurement channel gain independently to correct for this, or use the db +/- spinner to adjust the zero level of the displayed transfer function. Getting Started with SmaartLive: Basic Measurement Setup and Procedures Page 6

43 Performing the Transfer Function Measurement SmaartLive s Transfer Function mode measures a system s frequency response by comparing its input signal to its output signal. This measurement shows the difference between those two signals in both magnitude and phase and represents the processing behavior of the system as a function of frequency. Gain and loss show up as deviation from the center 0 db line on the magnitude trace. By adjusting filter settings on the equalizer, you should be able to see the changes being made in the frequency domain on the SmaartLive display. If attenuation (or cut ) on the equalizer shows up as a peak on the display, it is likely that you have inadvertently reversed the input signals. You can either physically swap the input cables or press the Swap button to reverse the signals and obtain the proper display. SmaartLive defaults to the FPPO (Fixed-Point per Octave) transfer function mode, which provides you with transfer function measurement points distributed equally on a logarithmic frequency scale by varying the FFT length at different frequencies. You may wish to experiment with different fixed-width FFT parameters, sampling rates, and excitation signals to see the effect of the various parameters. You may also press the Phase button to see the transfer function phase (in addition to magnitude) as a function of frequency. Figure 8 shows an example measurement of a single parametric equalizer filter, including the phase plot. Figure 8: Sample measurement of an analog parametric equalizer filter. Note that, for this measurement, we have not included any compensation for delay through the equalizer, since the delay through almost any analog equalizer will be insignificant relative to the length of the FFTs used in the calculations. When measuring a digital device, loudspeaker, or almost any electroacoustic system, we must first measure the propagation delay time and use SmaartLive s internal alignment delay to compensate for any delay in the external system. This will be covered in Example 3, Measuring a Loudspeaker. Getting Started with SmaartLive: Basic Measurement Setup and Procedures Page 7

44 Example Application 3 Measuring a Loudspeaker In this example, we will use both the Impulse and Transfer Function modes in SmaartLive to measure the behavior of a loudspeaker in a room. To perform this exercise, you will need a loudspeaker and power amplifier (or powered loudspeaker) in addition to your SmaartLive measurement system. Measurement Microphone Loudspeaker Microphone Preamplifier Line Input L R Computer with SmaartLive TM Line Output L R -or- Power Amplifier Figure 9: Hardware configuration for measuring a loudspeaker. Connecting the System Connect the system as shown in Figure 9 above. The output of the sound card drives the power amplifier and loudspeaker as well as the right input (the reference signal) of the computer as in the preceding example. For this measurement, however, a measurement microphone is used as the measurement signal, which is brought into the left sound card input via a microphone preamplifier. You will want to position the measurement microphone at a nominal distance from the loudspeaker, for example, 1m. The farther the microphone is from the loudspeaker, the more difficult it is to separate the direct sound of the loudspeaker from the influence of reflections in the room. Adjusting Signal Levels We must now adjust the signal levels to obtain a reasonable gain structure through the system. Enter SmaartLive s Spectrum mode by clicking the Spectrum button and turn the analyzer ON. As before, turn on the internal signal generator and adjust its level until the sound level from the loudspeaker is appreciably higher than the ambient noise in the room. You may wish to start with a low power amplifier gain and then slowly increase the level to prevent unexpectedly loud signals from reaching your ears. Next, adjust the input levels on the sound card and the microphone preamplifier gain to achieve a proper input level, following the guidelines in Figure 3. For best results, you will want to match the levels at the reference and measurement inputs as closely as possible, so adjust the preamplifier gain to achieve this. Performing and Interpreting an Impulse Response Measurement Now, we will perform a basic impulse response measurement of the loudspeaker in the room. Click the Impulse button to enter the Impulse mode; SmaartLive will automatically measure an impulse response of the system and display it in the graph window. You may make another impulse response measurement at any time by pressing the Start button. An example of what you might see is shown in Figure 10. Getting Started with SmaartLive: Basic Measurement Setup and Procedures Page 8

45 The impulse response in Figure 10 is quite typical of what you might see when measuring a loudspeaker in any non-anechoic room (any room with reflective surfaces). The impulse response view shows a time history of energy arriving at the microphone, and is Direct Sound very useful for understanding exactly what you are measuring. Figure 10 shows the Log magnitude Room Reflections view, which indicates the magnitude of the impulse Noise response in db. SmaartLive can also display the impulse response in Linear units (which preserves polarity information) and as an ETC (Energy-Time Curve), which extracts the decay envelope from the impulse response, displayed in db. The large peak at the beginning of the plot in Figure 10 indicates the arrival of direct sound from the loudspeaker, which Figure 10: Impulse response of a small loudspeaker in a room. in this case, is the component that interests us. SmaartLive automatically detects the time and magnitude of this peak, which, in this case, is arriving with a delay time of 2.29 ms. This delay is due to the propagation time from the loudspeaker to the microphone through the air over distance of approximately 2½ feet. We will use this concept in correcting for the propagation delay when we perform a transfer function measurement. The other energy shown in impulse response is due to reflections in the room and noise in the measurement. The noise floor can be seen to have a constant average level; the accuracy of your measurements is dependent upon an adequate signal-to-noise ratio between the direct sound and this noise level. Performing a Transfer Function Measurement of the Loudspeaker Next, we will measure the frequency response function of the loudspeaker using the Transfer Function mode in SmaartLive. Click the Transfer button to switch to the transfer function mode, and make sure the analyzer is running. We now need to set SmaartLive s internal delay to compensate for the propagation time between the loudspeaker and microphone. Click the Auto Sm (Delay Auto-Locator Small) button to do this; SmaartLive will run an impulse response measurement in the background and automatically measure the delay time. The Delay Found dialog box appears with the measured delay time; click Insert Delay to accept the shown delay time to compensate for the propagation delay during transfer function measurements. If the shown delay time seems impossibly long, you likely have the reference and measurement inputs swapped; simply swap the input cables and try again. This process may also be performed manually using the Impulse mode; click the Set Delay to Peak button in the impulse response mode to set the transfer function delay to the peak arrival time. You may use the delay presets feature to store several delay times for quick recall using the keyboard. This is useful if you are switching between microphones in different locations or between a measurement microphone and an equalizer, for example. To assign the current value to a present, click the Delay label above the delay readout field and then click on one of the five buttons labeled F6-F10 on the delay tab of the options dialog box. You may then recall this delay at any time by pressing the corresponding function key on the keyboard. Getting Started with SmaartLive: Basic Measurement Setup and Procedures Page 9

46 For this example click on the button marked F6 to store the current delay into the first preset. Press OK to exit the dialog box.with the analyzer running in transfer function mode, you should now see the frequency response of the loudspeaker (energy vs. frequency) displayed in the window as shown in the example measurement in Figure 11. You may find that the display is somewhat erratic; increasing the number of averages using the Avg spinner will stabilize the transfer function trace. Set the number of averages 16 or higher to see improved behavior. Saving a Measurement Trace using the Reference Registers Figure 11: Sample transfer function measurement of a small loudspeaker. SmaartLive s Reference Registers are used to capture and store snapshots of the active live trace. The Reference Registers are represented by five groups of small solid-color buttons, labeled A, B, C, D and E, located below the plot area. Click the button for register A1 (the first register button in the A group). This activates the register even if the button was already depressed. Click the Capt (Reference Capture) button below the plot area to sample and display the current trace as an overlay on the plot. Click the A button to remove the captured trace from the display. The sampled trace, called a Reference Trace will remain stored in the register until you erase it or capture another trace to the same register. To permanently save a Reference Trace to a file on disk, called a Reference File, click the Info button to the right of the capture button. This opens the Reference Trace Information dialog box. This dialog box has six tabbed pages. Click on the tab labeled A in the upper portion of the dialog box to bring that page to the front. Select the register containing the Reference Trace you just captured (by clicking the first of the four solid-color register buttons on the left) and click the Save button. This opens a Windows Save file dialog box prompting you to select a file name ending with the (*.ref) extension. Reference Files may be recalled later and displayed as traces by selecting a register in this same dialog box and pressing the Load button. You can also save and reload the contents of all 40 reference registers as Reference Group (*.rgp) files using the Save All and Load All buttons on the General tab of this dialog box. After saving the reference trace to a file, click the OK button to exit the Reference Trace Information dialog box. Note that when you capture a reference trace, the stored trace is initially displayed in front of the live trace on the plot. The text color in the db +/ spinner field to the right of the plot changes to match the reference trace color and when cursor tracking is enabled, the mouse tracking cursor follows the stored trace instead of the live trace. You can return the focus of the display to the live transfer function trace by clicking anywhere on either input level meter with your mouse. Getting Started with SmaartLive: Basic Measurement Setup and Procedures Page 10

47 Example Application 4 Equalizing a Loudspeaker In this example, we will use the transfer function measurement from Example 3 to set an equalizer to optimize the performance of the loudspeaker. To perform this exercise, you will need the equalizer in addition the loudspeaker and power amplifier from the previous examples. Measurement Microphone Loudspeaker EQ mic Line Input L R Computer with SmaartLive TM Line Output L R -or- Equalizer Power Amplifier Microphone Preamplifier Figure 12: Hardware configuration for equalizing a loudspeaker. Connecting the System Connect the system as shown in Figure 12 above. When compared to the last example, this configuration simply inserts the equalizer into the signal chain between the sound card output and the power amplifier. A return line is also included, which simply receives the signal that is present after the equalizer, allowing you to adjust the filters in real-time exactly as in Example 2. The switch shown on the left sound card input is simply to show that you will wish to select between the measurement microphone signal and the signal coming directly from the output of the equalizer. This may be accomplished in many ways, including the use of a small mixer, a physical switch, or by simply re-patching the input cables. Performing the Measurements and Setting the Equalizer We will assume that you have performed the measurement of the loudspeaker as described in Example 3, and that the transfer function trace from the measurement is stored in reference register A1 with the propagation delay time stored into the first delay preset (recallable by pressing F6 on the keyboard). If this is not the case, perform the measurements described in Example 3 before proceeding. Now, reconfigure the inputs such that the left or measurement input is taken from the output of the equalizer. Make certain that the input and output levels are appropriate and no clipping is present on any device. If you are using an analog equalizer, press F5 on the keyboard to reset the internal delay to 0 ms. If you are using a digital equalizer (and/or digital mixer), click the Auto Sm button to measure and insert the appropriate delay time into SmaartLive. Figure 13: Real-time inverted equalization filters (yellow) matched to the measured loudspeaker response (orange). Getting Started with SmaartLive: Basic Measurement Setup and Procedures Page 11

48 To equalize the system, we will calibrate the equalizer to have a frequency response that is approximately inverse to the response of the loudspeaker. In other words, the peaks in the loudspeaker response will correspond to equivalent nulls in the equalizer response, flattening the frequency response curve. We will use the stored reference trace containing the measured loudspeaker response as a template by which to adjust the equalization filters. Make sure that the reference trace containing the loudspeaker response measurement is active on the display (in this case, A1) by using the reference trace control buttons. Use the db +/- spinner to center the curve vertically near 0 db. Now, click the Swap button to invert the measured frequency response of the equalizer. Any cut filters will now be displayed as boosts, and vice-versa, which allows us to visually match the inverted equalizer response to the loudspeaker transfer function to optimize the equalizer settings. Now you may adjust the equalizer to best fit the inverted equalizer response to the measured loudspeaker transfer function (Figure 13). After the equalizer settings have been optimized, you may perform another transfer function measurement of the entire system Figure 14: Resulting equalized loudspeaker response after applying the filters from Figure 12. to see the final result (Figure 14). To perform this measurement, select the measurement microphone as the measurement input, and recall the appropriate delay preset by pressing F6 on the keyboard. As a practical note, boost filters are best used sparingly when optimizing the frequency response of a sound system. Excessive use of boost filters may destabilize a sound system by reducing gain-beforefeedback and/or headroom, as the nulls that you observe in measurements may not be present in all spatial locations (due to comb filtering from reflections, room modes, loudspeaker interference, etc.). If you find that you require a large number of boost filters or that any required filter is very narrow in bandwidth, your problem may not be best resolved through equalization alone. Correction of acoustical conditions, crossover settings, or loudspeaker arrangements may be necessary. Typically, electro-acoustical phenomena that produce wide bandwidth (low-q) peaks in frequency response are most effectively addressed through equalization. Additionally, we recommend the use of parametric equalizers for precision equalization, to enable the selection of proper bandwidth and center frequency for each filter SIA Software Company, Inc., Whitinsville, MA USA All rights reserved. Getting Started with SmaartLive: Basic Measurement Setup and Procedures Page 12

49 SIA-Smaart Application Notes The Fundamentals of FFT-Based Audio Measurements in SmaartLive Presented by: SIA Software Company, Inc A LOUD Technologies, Inc. Company

50 Copyright SIA Software Company, Inc. A LOUD Technologies, Inc. Company All rights reserved

51 The Fundamentals of FFT-Based Audio Measurements in SmaartLive Paul D. Henderson This article serves as summary of the Fast-Fourier Transform (FFT) analysis techniques implemented in the SIA-SmaartLive measurement platform. By reading through this document, you will receive an understanding of the fundamental concepts in FFT-based measurements used throughout the SmaartLive application, providing you with insights to better comprehend the measurement parameters, procedures, and resulting data. As a prerequisite to this text, you should be familiar with the basic concepts presented in the article Getting Started with SmaartLive: Basic Measurement Setup and Procedures. Time Domain Sampling: Getting Signals into SmaartLive Most of the acoustical and electrical signals that we may wish to measure are signals that are continuous, that is, they have a defined value for every possible instant in time. Sound pressure and analog voltage are two examples of continuous-time signals that we may wish to measure using our instrumentation. However, in order for these continuous signals to be analyzed using a computer-based measurement system such as SmaartLive, we must convert the signal into a stream of digital samples, with each sample representing a numeric value that is proportional to the measured signal at a specific instant in time. This process is called sampling: converting the continuous-time signal into a discrete-time signal (a process handled by an analog-to-digital converter in the computer sound card). The sampling process employed for SmaartLive measurements (and for most other purposes in digital audio) creates digital signal data spaced on an even interval of time. The number of samples per second is the familiar sampling rate (or sampling frequency), referred to here as SR in units of Hz. The sampling rate directly affects the highest frequency that we may analyze in the f = SR computer, conventionally called the Nyquist limit frequency (f max ), which is exactly equal to one-half the sampling rate. For measurements on electroacoustical signals and systems, we are most interested in signals that lie in the frequency band from approximately 20 Hz to 20 khz (the range of human hearing). Therefore, for most measurements, you will wish to choose the highest sampling rate compatible between your sound card and SmaartLive, typically either 48 khz or 44.1 khz, which will provide a measurement bandwidth of at least 20kHz. A parameter inversely related to the sampling rate is the sampling period (T) which refers to the length of time (in seconds) between samples. Our measurements will have a time resolution equal to T, meaning that we cannot discern any details from the time signal that have a duration less than this value. For example, if we use SmaartLive to measure signal delays by finding peaks in the impulse response, we cannot measure a time delay difference of less than T. In addition to the choice of an optimal sampling rate, we must also consider the word length of the analog-to-digital converter when configuring the measurement system. For every sample, the analog-to-digital converter must assign a defined digital bit pattern to represent the T max f max = Nyquist limit frequency (Hz) SR = sampling rate (samples/sec) SR = 1 T SR = sampling rate (samples/sec) T = sampling period (sec/sample) 2 The Fundamentals of FFT-Based Audio Measurements in SmaartLive Page 1

52 amplitude of the signal at that instant. In effect, the longer the word length, or bits per sample, the higher the dynamic range of the measurement. In addition (and perhaps more importantly), increasing the word length increases the amplitude resolution of the measurement, as the sampled amplitude steps are distributed on a smaller interval. Inexpensive sound cards may offer word lengths of 16 bits, with professional cards offering 24 bit input and output capability. As with the sampling rate, set the word length in SmaartLive to the maximum values compatible with your hardware. Quick Reference Sampling rate (SR) Sampling period (T) Word length The number of samples per second (in Hz) used in the conversion process. Sets the maximum frequency that may be analyzed (Nyquist=SR/2). Set to 48kHz or 44.1kHz in SmaartLive for most measurements. The time interval between samples, equal to 1/SR seconds. Time-domain details of duration less than T (sec) will be masked (delays, reflections, etc.). Number of bits used by the analog-to-digital and digital-to-analog converters in the sound card. Always use the maximum values compatible with your hardware. FFT Analysis: Viewing Frequency Domain Information While performing measurements in the time domain may be interesting and useful in many cases, we require more information for most audio measurements: spectral information, or knowledge about the frequency content and behavior of the audio signals and of complete systems. Fortunately, there exists a defined technique for converting, or transforming data from the time domain into the frequency domain, where information exists about the spectral content of signals. The Fourier Transform allows us to convert a time signal to the complex frequency domain, meaning the spectral data contains information about both the amplitude and phase of the sinusoidal components that make up the signal (see sidebar). In addition, the Fourier Transform provides us with an inverse transform, which allows us to convert the complex frequency-domain signal data back into the time-domain without losing information. Therefore, the both the time- and frequency-domain data are equivalent: the two domains simply provide a different view of the same signal (see Figure 1). SmaartLive uses a digital implementation of the Fourier Transform called the Fast Fourier Transform, or FFT, which is simply a computationally-efficient method for computing the Fourier Transform on digital signals. The FFT works on finite-length blocks of sampled data (called FFT frames). We will use the notation N FFT for the length of the FFT data frame in samples (or, equivalently points). From this value, we can easily compute the length of the FFT frame in units of time Optional Note: Fourier Theory The 19 th century French mathematician Jean Baptiste Joseph Fourier proposed a concept allowing us to express any time signal as a function of fundamental frequencies. Fourier theory states that any complex time signal, be it noise, speech, music, etc., is composed of a combination of sinusoidal waves of varying frequency, amplitude, and phase. We can use this basic concept as a transform, or a mathematical method for moving signals between the time and frequency domains. To convert a continuous signal x(t) to its frequency domain counterpart X(j? ), we may use the forward Fourier Transform: + jωt = x( t e dt X ( jω ) ) We may reverse this operation with no loss of information using the Inverse Fourier Transform: + = 1 j ω ω t x( t) X ( j ) e d 2π ω It should be noted that, in the most formal sense, the Fourier Transform requires the complete time history of a signal (for all time: an infinite-length view) and an infinite number of sinusoidal frequency components to fully describe a signal. This is, obviously, of no practical use for measurement, since we can only observe the signal for a finite amount of time. To implement the Fourier Transform computationally, we must utilize time windowing to limit our view of the signal to a finite frame of time. We may utilize the Discrete Fourier Transform (DFT), which operates on sampled-data signals, or the Fast Fourier Transform (FFT), which computationally accelerates the DFT. The Fundamentals of FFT-Based Audio Measurements in SmaartLive Page 2

53 using the sampling rate. We will call this value the time constant TC, representing the length of time that each FFT frame observes the continuous input signal. Higher the values of TC provide a longer time window in which we observe the signal, but also increase the time between subsequent updates of the FFT spectrum and the amount of numeric data that must be processed. TC = N FFT SR TC = FFT time constant (sec) N FFT = FFT size (samples) SR = sampling rate (samples/sec) Amplitude vs. Time Magnitude vs. Frequency System Response Voice Signal Time Waveform Amplitude vs. Time Time Domain FFT Inverse FFT FFT Inverse FFT Frequency Domain Signal Spectrum Magnitude and Phase vs. Frequency Impulse Response Transfer Function Figure 1: The Fourier Transform: moving signals between the time and frequency domains. Upper example shows the conversion between an impulse response and a transfer function; lower example is the conversion between a time signal (voice sample) and its spectrum. The FFT generates frequency domain data that is linearly-spaced as a function of frequency, unlike our hearing, which primarily perceives frequency in a logarithmic manner. Conveniently, the time constant TC is inversely proportional to the frequency resolution of the spectral data, referred to here as FR. The FFT spectrum will include complex frequency data (magnitude and phase) spaced on even intervals of FR FR = 1 TC FR = Frequency resolution (Hz) TC = FFT time constant (sec) extending from 0 Hz (DC) to the Nyquist frequency. With this concept, it is easy to see how resolution is inversely related between the time and frequency domains. Using longer FFT sizes provides higher- The Fundamentals of FFT-Based Audio Measurements in SmaartLive Page 3

54 resolution spectral data but more sluggish time response, while shorter FFT sizes provide lower spectral resolution but faster time response. Figure 2 graphically demonstrates the effect of changing the FFT parameters on resolution in the frequency domain. When distributing the linearly-spaced FFT data on a logarithmic axis, it can be easily seen that short FFT s may provide inadequate low-frequency resolution, while long FFT s may provide excessive high-frequency resolution. Frequency (Hz) (Linear Scale) Frequency (Hz) (Log Scale) Figure 2: The effect of FFT parameters on frequency resolution. Note that the FFT spectrum data is equally-spaced on a linear frequency scale but exponentially-distributed on a logarithmic frequency scale. This may yield inadequate low-frequency resolution for short FFT s and excessively detailed high-frequency resolution for long FFT s. Fortunately, we are not required to manually calculate the parameters that have been discussed here. The FFT Parameters function in SmaartLive allows for the independent selection of sample rate, FFT size, time constant, and frequency resolution. A change in any one parameter immediately updates the other dependent parameters, allowing the user to concentrate on the meaning of the values, not on their calculation. An indicator in the main SmaartLive window shows the active settings for the live input signals. Quick Reference FFT FFT length (N FFT ) Time constant (TC) Frequency resolution (FR) The Fast Fourier Transform, a method for moving digital signals between the time and frequency domains. The length of the FFT input data frame in samples. The length of the FFT input data frame in seconds, equal to N FFT /SR. Indicates the length of time that the FFT observes the signal in each data frame. The frequency resolution of the FFT spectral data, in Hz, equal to 1/TC. FFT data is linearly spaced from 0Hz to the Nyquist limit on even intervals of FR. Improving the Spectral View We have shown that the frequency domain spectral data from an FFT is distributed on a constant, linearly-spaced interval in frequency. If we evenly distribute the FFT data onto a graph, we will need to employ a frequency axis that is equally spaced in frequency, that is, there is an equal interval per Hz. In contrast, our hearing perceives musical pitch on (approximately) equal frequency ratios, yielding a logarithmic frequency axis for equal-interval analysis (an equal interval per octave). Obviously, if we The Fundamentals of FFT-Based Audio Measurements in SmaartLive Page 4

55 distribute the linearly-spaced FFT data on a logarithmic frequency axis, the apparent resolution along the frequency axis is not constant, possibly with insufficiently low resolution in the lower octaves, and inappropriately high resolution in the upper octaves (as seen in Figure 2). We can maximize the low-frequency resolution by increasing the FFT size, however, this leads to a longer time constant and, consequentially, slower time response. In addition, for transfer function measurements, the increased time window will also include additional room reflections in the measurement, potentially obscuring details in the response curve. Obviously, we require additional methods for viewing the FFT data in a perceptuallysignificant manner to better correlate the graphical data with human hearing. Fractional-Octave Banding The Spectrum mode banding technique provides an FFTbased approximation of analog Real-Time Analyzer (RTA) filters, which utilize electronics to separate the incoming spectrum into bands and then derive the RMS level of each band over time. The banded views in SmaartLive provide an accumulation of the total energy in each logarithmicallyproportioned band (just like a hardware RTA), so signals with constant power per octave (like pink noise) will result in a flat banded spectrum (see figure below). Signals with constant power per Hz (like white noise) will indicate a rising (+3 db/octave) banded spectrum. The banded spectrum view is very useful for identifying the generic frequency content of input signals, identifying feedback frequencies, and investigating room noise levels. However, system equalization and tuning procedures are best performed using the transfer function measurement mode. SmaartLive contains several methods for improving the logarithmic-frequency view of FFT data, which vary according to the analysis task at hand. For spectrum-mode data (where we are simply interested in the spectrum of the input signal), we may employ frequency-domain banding, which distributes the data into equally-spaced fractional octave bands. The spacing and, consequentially, the width of each band is selectable as either 1-, 1/3-, 1/6-, 1/12-, or Narrowband Log Spectrum 1/3-octave Banded Spectrum Pink Noise Spectrum: Note the apparent downward slope seen when viewed as a narrowband spectrum becomes a flat curve in the log-proportioned banded view. In this case, the banded view more accurately reflects the perceived timbre of the signal. 1/24-octave. Figure 3 compares the log-distributed FFT spectrum with the banded spectrum for an input signal. (a) (b) (c) Figure 3: Spectrum-mode frequency banding; (a) original FFT spectrum data distributed onto a log-frequency axis, (b) spectrum data displayed in 1-octave bands, (c) spectrum data displayed in 1/24-octave bands. In addition to the banding method for handling spectrum-mode signals, the Fixed-Point per Octave (FPPO) technique in SmaartLive is used for computing logarithmically-spaced Transfer Function (frequency response) data. In effect, the technique utilizes a measurement time window that varies as a function of frequency, utilizing a long time window at low frequencies (for narrow frequency resolution) and a successively shorter time window at high frequencies. This method has two main effects: the variable time window is well-correlated with the hearing perception mechanism defining the perceived The Fundamentals of FFT-Based Audio Measurements in SmaartLive Page 5

56 spectral quality of a loudspeaker operated within a room, and the variable analysis frame lengths provide frequency-domain data that is of equal density per octave, in this case, 24 points per octave. For most transfer function measurements in SmaartLive, especially those involving some acoustical path (a loudspeaker or sound system measurement), the FPPO view provides the best representation of the system response function. Beyond the inherent low-frequency advantages, the FPPO technique typically provides a more easily readable trace at high frequencies, in contrast to the fuzzy character of standard FFT data caused by excessive high frequency resolution (see Figure 4). (a) (b) Figure 4: Log-frequency transfer function analysis; (a) transfer function of a small loudspeaker using a 32k-point standard FFT, (b) measurement of the same loudspeaker using the FPPO technique. In SmaartLive s transfer function mode, an additional option exists for smoothing of the transfer function trace over a definable number of points. The smoothing function is, effectively, a moving average filter that is applied to the transfer function data before it is displayed in order to minimize the presence of jagged edges and discontinuities in the displayed data. You may select either 3-, 5-, 7-, or 9-point smoothing depths, which define the number of FFT data points surrounding an individual value that are averaged to derive the displayed value; higher numbers yield a more continuous visual curve. Figure 5 shows an example of smoothing applied to a transfer function measurement of a small loudspeaker. Trace smoothing is available for both standard FFT sizes and FPPO curves. (a) (b) Figure 5: The effect of curve smoothing on transfer function measurement display, 8k-point FFT; (a) measurement of a small loudspeaker with no smoothing, (b) the same data displayed with 9-point smoothing. The Fundamentals of FFT-Based Audio Measurements in SmaartLive Page 6

57 Quick Reference Linear frequency scale Logarithmic frequency scale Fractional-octave banding Fixed-Point Per Octave (FPPO) Trace smoothing FFT data is distributed on a frequency axis scaled on equal intervals per Hz. FFT data is distributed on a frequency axis scaled on equal intervals per octave, which corresponds to human pitch perception. Used to represent Spectrum mode signals in logarithmically-distributed bands, much like a hardware RTA. Bands may be 1-, 1/3-, 1/6-, 1/12-, or 1/24-octave wide. Performs Transfer Function mode analysis on logarithmically-spaced (1/24-octave) frequency bins. Enhances trace readability and correlation to hearing perception when equalizing systems. Further smooths Transfer Function mode signal traces for improved curve readability. FFT Frame Averaging to Improve Trace Validity While the signal for each FFT frame is viewed only for a finite amount of time (the length of the time constant, TC), we can modify the time response of the measurements by using frame averaging techniques. Effectively, averaging causes the current displayed FFT data to reflect some cumulative average between the current data and past FFT frames. By varying the depth and function of the averaging, we can achieve changes in the apparent time response for measurements. In SmaartLive s Spectrum mode, several options are available for configuring the averaging technique used for measurement. The spectrum mode contains options for FIFO (First-In/First-Out) averaging, where the last 2, 4, 8, 16, 32, 64, or 128 FFT frames are averaged with equal weighting, and the result is displayed (see Figure 6). These modes allow the user to fine-tune the averaging depth depending on the measurement task and input signals: higher averaging frame counts provide a slower time response, with lower numbers better approximating the instantaneous behavior of the signal. The spectrum mode also contains exponential averaging techniques, which are marked Fast, Slow, and Exp. The Fast and Slow settings reflect the standard damping of a sound level meter in the associated integration mode, which are most useful for performing repeatable, standardized measurements. The Exp mode allows for the exponential averaging half-life to be customized, allowing the exponential averaging modes to be useroptimized based on the measurement task. Finally, the Inf setting allows for an (effectively) infinitelength average of the input data, which provides a running, equal-weight average of all FFT frames since the last buffer reseed. This is useful for general noise-level analysis tasks and specialized uses in cinema optimization, etc. It should be noted that the spectrum-mode averaging is performed on the power spectrum of the input signal. 4-Frame FIFO Buffer Latest frame Oldest frame Figure 6: Displayed average 4-frame FIFO-based averaging example; the displayed curve is a function of the mean curve from the last N FFT frames. The Fundamentals of FFT-Based Audio Measurements in SmaartLive Page 7

58 Similarly, SmaartLive s Transfer Function mode contains averaging capability, which provides two primary functions: (1) it provides a variable time response (identical to the behavior seen in spectrum mode), and (2) it provides a mechanism for increasing the validity and signal-to-noise ratio of the transfer function measurement. By averaging transfer function measurement frames over time, the estimate of the system transfer function increases in precision, with any random noise effects being reduced. When using the FIFO-based averaging scheme, a doubling of the number of averages corresponds to a 3 db increase in the signal-to-noise ratio of the measurement. In addition to basic averaging depth options, the transfer function mode allows the user to select either RMS or Vector averaging types. The difference between these two modes is the transfer function measure that is being averaged; in RMS mode, the geometric mean of the transfer function magnitude is computed, whereas in Vector mode, the complex transfer function (including phase) is used for the averaging operation. Vector mode provides the most robust averaging technique for use in phase/time-invariant situations, where no wind gradients or rapid variations in the measured field are present. For most common measurements, however, RMS averaging provides a reasonably effective method of increasing the validity of the transfer function measurement with less sensitivity to these issues. It should be noted that, in RMS mode, the averaged phase trace is derived from a vector average; only the magnitude curve is obtained through RMS averaging. SmaartLive s Impulse mode utilizes an RMS-based averaging technique, which operates solely on a FIFO-style FFT frame buffer. As with the transfer function mode, increasing the averages by a factor of 2 corresponds to a 3 db increase in signal-to-noise ratio. The sole purpose of averaging in the impulse response mode is to improve data validity and reduce the impact of measurement noise, although higher averaging depths will directly correspond to longer acquisition times in this mode. Quick Reference Frame averaging FIFO averaging Exponential averaging RMS averaging Vector averaging Improves data validity and trace stability by deriving the displayed data from a running average of the current data and past FFT frames. The displayed data is an equal-weight average of the current input data with a finite number of past frames. Available FIFO lengths are 2, 4, 8, 16, 32, 64, or 128 frames. Provides an integrated averaging response similar to that of a sound level meter. Provided are Fast, Slow, and Exp (custom) response characteristics. Averaging behavior in this mode utilizes the geometric mean of the response data. Used in the Spectrum and Impulse modes and available as a option in the Transfer Function mode. Useful in Transfer Function mode when the system is varying in time (wind gradients, etc.). Averages the complex value of the transfer function data, providing maximum precision when the system is time-invariant. Measurement Time Windows We have noted previously that, for real-world measurements, the FFT is only able to observe the signal for a finite amount of time, which we may call the measurement time window. Beyond the basic observation that we may only draw conclusions about the signal from this narrow slice of time, this operation also creates anomalies in the frequency domain, which may lead to errors in the observed frequency spectrum. The Fundamentals of FFT-Based Audio Measurements in SmaartLive Page 8

59 Time Domain Frequency Domain amplitude db (a) time frequency amplitude db (b) time frequency amplitude db (c) time frequency Figure 7: Time windowing effects in the Fourier transform with a sinusoidal signal; (a) an infinite time window, (b) a finite Rectangular time window, (c) a finite Hanning time window. Figure 7 demonstrates the effect of a finite time window on the FFT spectrum of a sinusoidal (singlefrequency) input signal. A steady-state sinusoidal signal has energy at only one unique frequency, so the ideal spectrum produced by the Fourier transform should indicate this by an infinitely narrow line at that frequency. As shown in Figure 7a, the Fourier transform is able to accurately determine the spectrum, given an infinite time record of the signal. However, if we reduce our view of the signal to a finite-length FFT frame, we, in effect, multiply the time signal by a rectangular window, as shown in Figure 7b. The effect of this windowing operation on the frequency domain is obvious, as the energy is dispersed into a single main lobe plus a number of side lobes (called spectral leakage). The pattern of the side lobes is a function of the rectangular window, and is primarily created by the abrupt discontinuity at the edges of the window. The high relative level of these side lobes could cause other important spectral information to be hidden, or masked. However, if we apply a finite but gentle time windowing function, as seen in Figure 7c, we can significantly reduce the level of the side lobes by gradually tapering the waveform to zero at the ends. A side effect of this operation causes the main lobe to increase in width, which may also mask spectral details from nearby frequency components. We can balance the side lobe magnitude and pattern against the main lobe width by careful selection of the windowing function, which can be customized depending on the analysis task. SmaartLive contains a number of time windowing functions which provide varying characteristics in time and frequency. For more information, see the SIA technical note The Mystery of Data Windows, which covers this topic in further detail. Optimal FFT Parameter Settings for SmaartLive This section will provide suggestions for reaching the optimal FFT parameter settings depending on the measurement task at hand. As each parameter is highly configurable, a general set of criteria is presented here that allow you to optimize the measurement system depending on the desired temporal and spectral The Fundamentals of FFT-Based Audio Measurements in SmaartLive Page 9

60 resolution. For most uses, once an optimal set of parameters is reached for a specific measurement task, the FFT parameters may be left unmodified for subsequent measurements. A parameter that will not be specifically addressed as a variable is the selection of an optimal sampling rate, which defines the highest measurable frequency (Nyquist) and the time resolution of the measurement. As noted previously, you should typically select the highest compatible sampling rate between SmaartLive and your hardware interface, usually either 48 khz or 44.1 khz. On rare occasion this guideline may be modified, such as those situations requiring a lower-bandwidth measurement where computational power may be conserved by choosing a lower sampling rate. Spectrum Mode For most real-time analysis measurements in Spectrum mode, we are primarily concerned with three major criteria: appropriate spectral resolution for the target measurement, an appropriate response characteristic in time, and a reasonable correlation to human hearing perception. We may use these basic criteria to develop guidelines for choosing FFT parameters in this mode. Spectrum Mode You may wish to begin with these parameter settings: In spectrum mode, the FFT size should be configured for an optimal trade-off between low-frequency resolution and time response. A good starting point may be to choose a 16k-point FFT frame, which tends to provide acceptable frequency resolution with an ~350 ms time constant (at SR = 48 khz) for a reasonable time response characteristic. For detecting dynamic changes in signals, a Fast averaging characteristic is useful, with the Slow setting more useful for analytical measurements (noise, etc.). Of course, you may experiment with different FFT parameter settings to optimize performance. For most measurements in this mode, you will wish to choose a banded display; a 1/3-octave display is a good starting point for many measurements, as it corresponds to the critical bandwidth of hearing perception for most complex signals. Higher resolution displays may be used to more accurately detect spectrum details, such as feedback center frequencies, etc. Transfer Function Mode Most transfer function measurements fall into one of two categories: measurement of the electrical transfer function of a device (an equalizer, etc.), or measurement of the electroacoustical transfer function of a complete system (a loudspeaker, sound system, etc.). For most electrical measurements, choosing a standard linearlyspaced FFT is typically a good starting point. Note that, for proper measurement of low-frequency filters, the FFT parameters chosen should have sufficiently narrow frequency resolution (start with 16kor 32k-point FFTs). Electrical measurements typically provide an inherently high signal-to-noise ratio, so a short averaging time (8-16 averages or the fast response characteristic) may be used for a more dynamic time response. Transfer Function Mode You may wish to begin with these parameter settings: Electrical measurements Acoustical measurements The Fundamentals of FFT-Based Audio Measurements in SmaartLive Page 10

61 When performing electroacoustical measurements, the FPPO measurement mode should typically be used for best results. FPPO will best approximate the hearing perception of spectral effects in most electroacoustical systems and is typically far easier to interpret than standard FFTs due to the natural fractional-octave distribution of data. Electroacoustical measurements are far more susceptible to noise and time variance effects, so the use of a long averaging time is recommended (64+ averages or the slow response characteristic). In addition to these parameters, the transfer function mode contains coherence and magnitude threshold settings, which may used to ensure valid data. Typical settings for these parameters when performing electroacoustical measurements are: coherence threshold = 10-15%, and magnitude threshold = 35-55%. The details of these parameters are outlined in following articles, and in the SmaartLive User Guide. Impulse Response Mode Selecting appropriate FFT parameters for the Impulse mode is somewhat more straightforward than for other modes in SmaartLive. Two primary criteria are at work for impulse response measurements: the decay time of the measured impulse response and the effective signal-to-noise ratio of the measurement. For effective impulse response measurements, the time constant TC must be greater than the total decay time of the system under test in order to assure valid data. In performing impulse response measurements, it is often difficult to obtain an acceptable signal-to-noise ratio in order to fully view the entire decay of the system. As with transfer function measurements, increasing the number of averages will increase the effective signal-to-noise ratio of the measurement. An identical effect is seen by simply increasing the time constant; this provides an equivalent increase in the time the system is observed in order to increase the signal-to-noise ratio. Other methods exist for lowering the noise floor, such as increasing the acoustic level of the stimulus or by carefully selecting the stimulus signal type (such as using synchronized sinusoidal sweep signals). These advanced concepts are discussed in subsequent articles, as well as in the SmaartLive User Guide. Impulse Mode You may wish to begin with these parameter settings: Note: Increase FFT size such that TC exceeds the system decay time. You may increase the FFT size, averaging depth, and the stimulus level to maximize the signal-to-noise ratio of the measurement. Suggestions for Further Reading If you have an interest in furthering your knowledge of the engineering concepts behind FFT-based measurement, you may find the following texts useful: A. Oppenheim, A. Willsky, S. Nawab: Signals and Systems, 2 nd edition. Upper Saddle River, NJ: Prentice Hall Inc A. Oppenheim, R. Schafer, J. Buck: Discrete-Time Signal Processing, 2 nd edition. Upper Saddle River, NJ: Prentice Hall Inc The Fundamentals of FFT-Based Audio Measurements in SmaartLive Page 11

62 NOTES

63 SIA-Smaart Application Notes Spectrum Measurements with SmaartLive: Concepts and Applications Presented by: SIA Software Company, Inc A LOUD Technologies, Inc. Company

64 Copyright SIA Software Company, Inc. A LOUD Technologies, Inc. Company All rights reserved

65 Spectrum Measurements with SmaartLive: Concepts and Applications Paul D. Henderson A key component of the SmaartLive application is its Spectrum mode, which provides a highly flexible FFT-based real-time analyzer capable of advanced audio signal measurements. The spectrum mode is useful in many applications, including noise and sound exposure measurements, the location of feedback frequencies in sound reinforcement, and cinema system optimization, as well as general signal monitoring tasks. This document serves as an introduction to effectively applying the Spectrum mode measurement capabilities. A general knowledge of the topics covered in Getting Started with SmaartLive and The Fundamentals of FFT-Based Audio Measurements in SmaartLive will be helpful when reading this text. I. Basic Spectrum Analysis The real-time analyzer, or RTA, is a familiar tool to audio professionals, allowing the user to view the spectral content of audio signals throughout a system. Traditionally, RTAs were constructed as dedicated hardware devices, capable of displaying signal power versus frequency in fractional-octave bands. In early devices, banks of analog filters separated the spectrum into constant-percentage bandwidth subbands, and a level detector circuit was used to drive the unit s display. The result was a limited-resolution frequency domain view of the spectrum of the incoming signal (Figure 1), akin to the limited-time view provided by an oscilloscope. Amplitude Frequency Figure 1: Traditional real-time analysis: fixed & limited resolution. SmaartLive provides an advanced alternative to traditional RTAs, taking advantage of the computational efficiency afforded by the Fast Fourier Transform (FFT) and digital signal processing. SmaartLive has the capability to provide a much higher spectral resolution than filter-based approaches, and can simultaneously acquire a temporal signature of spectral changes over time. SmaartLive can display the fine structure of the linear-frequency FFT spectrum of the input signal or may be configured to show a fractional-octave (banded) view with similar response to a hardware RTA. This section will introduce the various measurement techniques used throughout the Spectrum mode, specifically targeting those measurement tasks that do not require an absolute-level calibration. Several applications are reviewed, including monitoring and troubleshooting of audio equipment and the location of electroacoustical feedback frequencies. Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 1

66 Monitoring Audio Signals For this application, we will investigate the use of the Spectrum mode to view the frequency content of generic audio signals, such as those received by a microphone or output by a mixing console. Figure 2 shows a simple measurement configuration for this task, where SmaartLive monitors the output of both a microphone preamplifier and a mixing console. While a simple configuration, the connection diagram in Figure 2 is a powerful tool for use in sound reinforcement, as SmaartLive may be instantly switched between the Spectrum and Transfer Function modes for quick access to information for both equalization purposes (the transfer function) and the live signal spectrum. Measurement Microphone Microphone Preamplifier Line Input L R Computer with SmaartLive TM Mixing Console Figure 2: Monitoring microphone and mixing console signals. Basic RTA Use If we launch SmaartLive with its default parameters and start the Spectrum mode, we will see a graph representing the signal power-versus-frequency in 1/12 th -octave frequency bands for both input channels (see Figure 3). You will note that the time response of the RTA display is quite fast; this is due to the short time constant (186 ms) and the fact that there is no frame averaging applied to the display (averages = 1). A fast time response is useful only for very specific applications, primarily when a joint time-frequency analysis of a signal is desired, such as with a spectrograph (as we will see later). This short time constant also provides minimal lowfrequency resolution, where the frequency resolution in this case is Technical Note The exponential averaging modes in SmaartLive conform to the ANSI S standard, where the exponential time constants t are as follows: Fast: Slow: t = 125 ms t = 1000 ms Figure 3: Default live RTA spectrum display (1/12 th -octave). Green curve: microphone, blue curve: mixer output. 5.4 Hz. As you can see in Figure 3, the low-frequency bands seem to have a smooth appearance, due to the low density of FFT data bins at these low frequencies. To improve the spectral view, we can increase the FFT size and use frame averaging to adjust the time response of the display. Changing the FFT size to 16k-bins and the averaging to slow Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 2

67 provides both additional low-frequency resolution and a more stabilized time response. The slow characteristic is based on a running exponential integration, and is useful for continuous signal monitoring during a live performance, noise level measurements, etc. The fast characteristic provides a much more immediate time response, and is useful for viewing transient signal information, such as specific musical notes. Note that the spectrum mode also allows for FIFO-style frame averaging, but, in most cases, this averaging technique is seldom required or recommended for Spectrum mode measurements. Note that both banded (1/24 th, 1/12 th, 1/6 th, 1/3 rd, and 1/1-octave) and narrowband (linear- and log-spaced) views are available. For a more detailed treatment of the FFT, averaging, and banding parameters, please see the article The Fundamentals of FFT-Based Audio Measurements in SmaartLive. You will note that, by default, the Spectrum display shows two separate traces, one for each input channel. SmaartLive contains a set of simple controls for managing the display of the two input channels, located directly underneath the input signal level meters. You may define either of the two input channels as the active channel by clicking the active indicators below the level meter. The current active trace will be brought to the front of the spectrum display, and the SPL Meter, SPL History Graph and Spectrograph displays will reflect the input signal from this channel only. The color of each of these displays will change to reflect the currently active channel. When using these advanced functions, it is important to note that the appropriate input channel is selected as active in order to obtain valid data. In addition, clicking the show/hide channel buttons will enable or disable the display of the associated spectrum in the RTA window. Set active trace Show/hide traces By default, traces in the RTA view contain peak hold bars, which hold the maximum value of the measurement parameter at each band or bin for a specified period of time. The configuration parameters for the peak hold mode may be found in the Input Options dialog box, which may be launched with the menu command Options? Input, or by pressing the key combination Alt+I. The hold time can be customized or an infinite hold mode may be activated, which holds the detected peak levels for an indefinite period of time until the next buffer reseed (performed by pressing the V key on the keyboard). In addition, the peak hold bars may be removed from the display for a more continuous, orderly appearance. By hovering the mouse pointer over the RTA spectrum, the level and center frequency of the selected band is shown in the readout above the trace display. In addition to this function, SmaartLive can display the musical note associated with the band center frequency using Note ID mode. Note ID mode may be toggled using the View? Note ID menu item. In addition, a reference piano keyboard may be activated using the Graph Options dialog box, accessible under menu item Options? Graph. You may use SmaartLive s reference trace functions to save a snapshot of the measured spectrum to a storage register for later recall and on-screen comparison. SmaartLive contains five reference registers (A, B, C, D & E), each capable of storing up to four individual traces. As an example, clicking the button for register A1 (the first register button in the A group) will activate this memory location. Click the button below the plot area to sample and display the current trace as an overlay on the plot. Note that the curve that will be captured is the current active trace, as defined above. The reference register stores the raw, post- Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 3

68 averaging FFT data, so the curve may be later viewed using any desired fractional-octave banding or narrowband display scheme. Viewing a Long-Term Spectrum Average The averaging buffer may be set to Inf, which will provide an equal-time-weighted average of the entire signal spectrum since the last buffer reseed. This method can provide you with a view of the longterm spectrum of the signal, a measure of the spectral signature of the input signal. For example, the 1/3 rd -octave spectrum in Figure 4 is a long-term average of a musical performance. This technique is also useful for capturing a stable measure of the continuous noise level in a room, which will be discussed later. Note that pressing the V key on the keyboard will reseed the averaging buffer, restarting the infinite averaging procedure at any desired time. Figure 4: 1/3 rd octave long-term spectrum of a musical performance. Performing Harmonic Distortion Estimates An interesting and sometimes-overlooked feature of SmaartLive s Spectrum mode is its capability to perform a rough Total Harmonic Distortion or THD measurement at a single frequency. THD is a metric used to quantify the nonlinear distortion of a system or device. A system with nonlinear distortion will output multiple frequencies for a single-frequency (sinusoidal) input, where those output frequencies will be multiples (or harmonics) of the input signal. This is typically due to a nonlinear transfer characteristic between the system input and output, which can be caused by tape saturation, digital clipping, transistor saturation, or nonlinear effects in loudspeakers. SmaartLive s THD capability is useful for quantifying the distortion measure of analog recording devices and power amplifiers, as well as for determining a (rough) distortion metric for loudspeakers. For this measurement, you will need to use SmaartLive s internal generator to output a single-frequency tone into the device-under-test at a reference frequency, and a low-distortion audio interface. The measured THD will represent the total distortion of the entire measurement system, so it is imperative that the measurement system have significantly lower distortion than the device under test. Figure 5 shows an example configuration, where a THD measurement of a loudspeaker is being performed. By placing the RTA in 1/24 th -octave resolution mode and activating the menu item under View? Cursor? Show THD, SmaartLive will calculate the total harmonic distortion from the amplitude of the fundamental and subsequent harmonics at the current cursor Figure 5: Sample THD measurement of a small loudspeaker at 200Hz: THD=0.12%. Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 4

69 position. Set the generator to Sine Wave to output a single frequency of choice, and place the cursor at that frequency. It may be necessary to increase the FFT size to maximize the low-frequency resolution of the measurement. Figure 5 shows a sample measurement of a small loudspeaker at 200Hz. For the measurement of a loudspeaker, the room should be very quiet, and a low-distortion microphone should be employed. Note that you may also use the Show Harmonics feature of SmaartLive by pressing Ctrl+H, which will activate a grid marking the harmonics relative to the locked cursor position. See the SmaartLive User Guide for more information. II. Viewing Spectral Changes in Time: the Spectrograph Many audio signals that are encountered in the field are highly dynamic: musical signals, speech, and even environmental noise contain significant changes in spectral content as a function of time. While the classical RTA spectrum display is useful for viewing the time-averaged spectral content of a signal, a display technique is required to enable the analysis of the incoming spectrum over time. SmaartLive s Spectrograph mode fulfills this requirement, providing a three-dimensional view of the incoming signal: energy versus frequency versus time (Figure 6). The spectrograph can be thought of as a record of multiple RTA spectrums taken over time, with color representing amplitude. Using this functionality, the spectral content of the input signal is recorded as it changes in time, allowing the user to view and analyze time-varying trends in the input signal. The Spectrograph display is launched while in Spectrum mode by pressing the button. Note that the Spectrograph display is derived from the current active trace. Figure 6: An example spectrograph of a musical performance. As a troubleshooting tool, the Spectrograph mode is useful for finding spectral defects in a system or acoustical environment. Certain audio signals or acoustical events contain specific traits that can be easily detected due to their distinct time/frequency signature, specifically, highly tonal sounds such as AC line noise in an electrical signal chain or the presence of electroacoustical feedback. Configuring the Spectrograph In order to achieve optimal results with this measurement mode, the Spectrograph configuration options must be properly set up for the measurement task at hand. The input banding, color range, and time averaging options are critical to achieving readable displays with this mode. The Spectrograph Options dialog may be launched using menu item Options? Spectrograph or by clicking the Spectro Range scale indicator. This dialog allows you to configure the color scale and amplitude range as well as the frequency and time axis Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 5

70 behavior. When configuring the spectrograph, the following issues are important to note: Spectrum banding: The banding scale of the spectrograph display tracks the selected banding of the RTA. For most applications, a 1/24 th -octave or log-narrowband scale provides the best broadband frequency resolution. Low fractional-octave resolutions typically result in a rough appearance. Time response: By default, the time response of the spectrograph display tracks the averaging depth selected for the RTA. However, excessive averaging (or averaging at all) can obscure time-based details in the spectrograph, such as in Figure 7b. For most applications, check the Instantaneous Spectrograph box in the Spectrograph Options dialog. With this option, each spectrograph frame will represent a minimum-width time slice of the input signal, improving the time response of the display (Figure 7a). In addition, the number of FFT frames contained within the spectrograph may be set in the Frames to show in Spectrograph field. Higher numbers yield a slower time response, with more time history contained within the window. Conversely, lower numbers produce faster movement along the time axis. The absolute-time length of the time axis is a function of this value and the speed of your computing hardware. Amplitude range: It is imperative that an appropriate amplitude range be selected in order to reveal the desired amplitude details from the input signal. The current range is configured using the Min db and Max db boxes in the options dialog. Selecting too large an amplitude range may obscure amplitude details by plotting a minimal change in color as the input spectrum changes (Figure 7c), and too narrow a range or values too high or low may lead to undershoot and overshoot errors (Figure 7d). The selection of an appropriate scale will enable the detection of spectral details with high definition in amplitude, as in Figure 7a. See the SmaartLive User s Guide for information regarding additional configuration options for the spectrograph display. (a): Instantaneous spectrograph, acceptable magnitude range calibration & good time resolution (b): Slow-weighted time response, time-domain details lost (c): Magnitude range too wide, amplitude details lost (d): Signal exceeds maximum magnitude range limit, peaks lost in clipping (white regions) Figure 7: The effect of selecting various spectrograph parameters; 1/24-octave banded spectrograph of an identical input signal. Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 6

71 Locating Feedback Frequencies in Sound Reinforcement Here, we will discuss the use of SmaartLive in determining electroacoustic feedback frequencies in sound reinforcement and/or stage monitoring systems. The location of feedback frequencies during live sound performance is a task especially well-suited for the Spectrograph mode, which provides an advantage to detecting the unique time/frequency signature of feedback ring tones. Microphone Stage Monitor Acoustical Environment Equalizer Power Preamplifier Mixing Console Line Input L R Computer with SmaartLive TM Figure 8: Finding feedback frequencies in a stage monitoring system. Figure 8 shows a simplified stage monitoring system with SmaartLive configured to monitor the console output signal before the equalizer. On a practical note, this connection can be made on the console s wedge output with access to the solo bus, so that any monitor output send can be retrieved immediately. A typical optimization process for a stage monitor system would entail an accurate equalization process using SmaartLive s Transfer Function mode, followed by in-show dynamic equalizer changes based on feedback modes that may be found as the acoustical environment varies. Note that a feedback mode in an electroacoustical system needs two components to begin ringing (or regenerating): a system-borne instability at any frequency and ambient sound energy at that frequency to initiate the regeneration. Therefore, it is imperative to note that using any method to locate feedback frequencies (commonly known as ringing out a system) without active signals in the system (such as a live performance) will result in inaccurate adjustments. If this process is performed without ambient sound such as in a preshow configuration, some broadband energy should be introduced to the system (such as low-level pink noise). Electroacoustical feedback is created by narrowband loop-path instability, and is primarily a single-frequency effect, although multiple feedback modes may be excited simultaneously. Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 7

72 Feedback Signature Figure 9: Feedback signatures in spectrograph and spectrum displays. This time-domain element of the spectrograph can be exploited in the task of finding feedback frequencies, since the ringing of electroacoustical feedback has a time-domain signature, i.e., it is constant in frequency and has both a duration and envelope in time. Narrowband constant-frequency signals such as a feedback ring tone or tonal noise source show up as horizontal lines in the spectrograph, making it somewhat easier to find these effects in the presence of a more complex signal, such as a live musical performance. Figure 9 illustrates this effect, as well as the simultaneous use of the spectrograph and RTA displays. An additional advantage of this technique is that the operator can immediately reduce the gain to eliminate the feedback loop on the console, and the running spectrograph will contain a history of the ring frequency for subsequent equalization changes. Note that, when controlling compatible external signal processors, their control parameters may be changed without leaving Spectrum mode. A Control frequency response display will appear, allowing you to view calculated EQ traces for compatible devices just as in the Transfer Function mode. III. Performing Calibrated Measurements For the measurement procedures introduced in Section I, SmaartLive was in its uncalibrated state: the values displayed were relative to the maximum full-scale range of the analog-to-digital converter. However, some measurement procedures require absolute calibration, where the displayed values are calibrated relative to real-world physical quantities. While SmaartLive can be calibrated to any decibelbased scale (dbu, dbm, etc.), the most commonly-used absolute scale is db-spl. Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 8

73 Calibrating the System for SPL Measurement Calibrator Measurement Microphone Microphone Preamplifier Line Input L R Computer with SmaartLive TM Figure 10: The SPL calibration process. In Spectrum mode, the entire system can be calibrated in a single step, including the built-in sound level meter. Several techniques are outlined in the User Guide for performing the calibration, but we will cover only the most accurate and widely-accepted procedure, which utilizes a sound level calibrator as an absolute level reference (see Figure 10). The calibrator should be correctly sized for your measurement microphone in order to ensure an airtight seal with the capsule. Most calibrators output a 1 khz Technical Note 0 db-spl = 20 µpa RMS 94 db-spl = 1 Pa RMS 104 db-spl = 3.2 Pa RMS 114 db-spl = 10 Pa RMS reference tone at one of the following reference levels: 94, 104, or 114 db-spl. Choose an appropriate reference level and adjust your microphone preamplifier gain to achieve sufficient headroom with this reference pressure. Place SmaartLive into 1/3 rd -octave RTA mode. The 1/3 rd octave mode is employed to make certain that all of the energy from the windowed sinusoid is taken into account. If calibration is performed in a narrowband or highresolution mode, the time window effects may distribute a significant portion of the sinusoid energy into surrounding bands. Select the input channel from the microphone as the active channel. Next, double-click on the 1 khz band (or other band if your calibrator uses a different center frequency), and the Amplitude Calibration dialog will open. Select Set this value to... and enter the level of your calibrator. The system is now calibrated to Sound Pressure Level for the current channel only, unless a microphone and preamplifier with identical sensitivity and gain are connected to the opposite channel. Note that any change in the preamplifier or sound card gain will necessitate recalibration. If the clip indicators in SmaartLive illuminate during use, reduce the preamplifier gain and recalibrate for additional headroom. Measuring Sound Pressure Level Now that the system is calibrated to SPL, we can perform accurate sound level measurements in any environment. You will note that the digital readout above the input level meters now displays db-spl with a Fast integration time. By clicking on the readout, you will be taken to the SPL Readout Options dialog, which enables you to configure the SPL meter component with various weighting curves and integration speeds, as well as configuration options for peak hold, SPL alarms, and logging capabilities. The peak hold and alarm functions are quite useful for live sound and noise level monitoring tasks, helping to maintain compliance with noise ordinances and safety regulations. The following sections will discuss the available weighting curves and integration speeds and their appropriate uses. Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 9

74 Weighting Curves For measuring sound pressure levels, SmaartLive includes three available weighting curves. A weighting curve is a filter response that is placed in-line with the SPL meter detector before the displayed value is calculated; the filter allows the response of the detector to vary as a function of frequency. SmaartLive contains Flat, A and C weighting filters, whose frequency response curves are shown below in Figure 11. The Flat weighting curve is exactly as the name implies: it has a perfectly linear response over frequency, meaning that the SPL meter will respond equally to equal acoustic pressure at any frequency inside its range. The Flat characteristic is useful for determining the total sound pressure at a point in space, as well as for sound power estimation tasks (beyond the scope of this document). The A and C weighting curves are drawn from the ANSI S standard. The C weighting curve contains a slight high-frequency and lowfrequency rolloff, meaning that the SPL meter detector is less sensitive to energy in those regions of the spectrum. The A weighting curve contains a much more dramatic low-frequency rolloff, indicating a primary sensitivity in the region above 1 khz. Often, the background work that leads us to these specific curves is overlooked: the A and C curves are approximate inverses of the equalloudness contours of human hearing at the 40 phon and 100 phon contour levels, respectively. The science behind the equal-loudness contours will not be presented here, but, suffice it to say that the A weighting curve approximates the response of human hearing at low levels, and the C weighting curve does the same at high levels. Magnitude (db) Frequency (Hz) Figure 11: SPL weighting curves. Flat Weighting A Weighting C Weighting Most noise level measurement standards have taken the A weighting function as customary, as, even at high levels, it more correctly approximates both the annoyance level of the noise and the potential for hearing damage. It should be stated that the suffix dba is commonly attached to sound pressure readings in the A weighting scale, and similarly dbc for the C weighting scale. Flat-weighted measurements are typically suffixed with db-spl. Integration Speeds SmaartLive contains three integration speeds for the SPL display: Inst, Slow, and Fast. The Inst setting effectively corresponds to the Impulse setting on a typical high-end sound level meter, as it displays the latest SPL data from the sound card with no averaging integration. This setting can be combined with the Peak Hold function to capture the peak sound level in an environment, specifically where there are impulsive and transient noise sources. The Fast and Slow settings are ANSI-standard exponential integration curves. The Fast setting is useful for finding standardized peak sound levels, again, best with the Peak Hold function or in conjunction with the SPL logging plot (to be discussed later). The Slow setting is perhaps the most useful for typical measurements, as it provides a longer integration time for more accurately representing the average sound level in the environment. The Slow response is also widely accepted in standards for studies in sound exposure and noise pollution (such as during a live performance). Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 10

75 SPL Time History and Logging Sound Exposure Data While SmaartLive is capable of monitoring SPL in real time, many measurement tasks require a more thorough investigation using the time history of sound levels in the environment, specifically when there are dynamic changes in the sound pressure. Many sound fields that humans encounter are highly dynamic, such as musical performance, industrial noise, etc. SmaartLive contains several tools to assist the user in this area, which include a run-time SPL History graph and logging functions capable of documenting overall sound pressure levels, spectrum histories, and SPL statistical metrics (L EQ, L X, etc.). This section will briefly overview a few applications for these capabilities. Using SPL History SmaartLive s SPL History function (Figure 12) is useful for real-time monitoring tasks, particularly during live musical performance. It is simply a running history of the SPL meter display on a per-frame basis (not including peak hold), and is directly affected by the weighting and integration speeds selected for the SPL meter. The SPL History display also shows the alarm threshold levels that have been preset for the SPL meter. You may configure the effective speed of the display by setting the number of shown frames in the options dialog by accessing the menu item Options? SPL History. This display is highly useful for monitoring sound levels in live performance, specifically with regards to maintaining both safe listening levels and compliance to noise ordinances and venue regulations. The detection of peaks is also very valuable, since the display will hold the peak envelope for a period of time, making it unnecessary to continuously watch the SPL meter readout. Figure 12: SPL history display. Logging Sound Exposure Statistics In addition to the SPL History functions, SmaartLive contains more advanced sound level statistics functions enabling the user to determine industry-standard sound exposure statistics. SmaartLive allows the user to both log SPL data to a file and to perform automated calculation of sound level statistics (L EQ, L X, L MIN, and L MAX ). Here, we will cover the use of the automated statistical functions; documentation for the simple logging capabilities is provided in the User Guide. Often in environmental noise studies or sound exposure analysis for live performance, a single-number SPL value does not sufficiently describe the variations in sound level. However, a complete time history of pressure levels is surplus information, so a compact, statistical description of the characteristics of the sound field level is required. Equivalent Sound Level, or L EQ, is the sound level that, if the sound field were continuous and single-level, would contain the same energy dose over the sampling time as the measured dynamic field. Percentile Noise Levels or L X, indicate the level that the sound field exceeds for Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 11

76 X-percent of the time; for example, an L 90 value of 82 dba indicates that the sound level is above 82 dba for 90% of the measurement period. SmaartLive automatically calculates the three most common percentile statistics, L 10, L 50, and L 90. Each of these values is based on the total duration of observation, which is configurable in the Sample Period field under the LEQ Setup dialog box. This dialog is launched through by clicking on the SPL meter display and then clicking on the Timed Average / LEQ Setup button. The automated LEQ Log option creates text files of the format shown in Figure 13. In addition, L EQ analyses may be derived from Spectrum Log files using the Create LEQ report from log file option, which also allows for custom percentile categories. ;LEQ ;A Weight ;Date Time LAEQ LAMin LAMax LA10 LA50 LA90 06/15/ :36: ; ;Cumulative Values 06/15/ :36: Figure 13: Sample L EQ analysis output file. Various national standards exist for sound exposure, specifically those for occupational safety, including those by OSHA and NIOSH. The OSHA-standard thresholds are typically considered somewhat highrisk, but are reprinted here in Table 1. NIOSH specifically recommends that the Time-Weighted Average for occupational noise (in effect, L EQ with an observation period of 8 hours) be less than 85 dba. Measuring a Calibrated Sound Spectrum The calibration process not only scales the SPL meter component to read absolute SPL values, but also causes the RTA Spectrum display to be calibrated to absolute SPL. This is particularly useful for fractional-octave band measurements, which indicate the total sound power in each band for advanced analysis tasks (see Figure 14). Note that, for narrowband signals such as a sine wave, the chosen fractional-octave bands must be wide enough to contain all significant energy from Duration per day Sound level Hours dba, slow response ½ ½ 110 ¼ 115 Table 1: OSHA standard ( ) for occupational noise exposure. Figure 14: Octave-band spectrum calibrated to absolute SPL. Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 12

77 the sinusoid, including the leakage energy from the time window operation. This is the same reason that a 1/3 rd -octave band scale is recommended for SPL calibration with a pure tone calibrator. You can see this effect by measuring a sine wave in narrowband Log mode; the peak value of the narrowband plot will be less than the total power of the input sinusoid. For broadband signals, such as pink noise, you will note that the individual level of each fractional-octave band decreases as the width of each band becomes smaller. This is due to the fact that less total energy is contained in each band as the bands become narrower. Room Noise Measurement The calibrated spectrum is useful for determining room noise levels in consulting practice and for documenting the background noise characteristics of a room. Spectrum measurement techniques are useful for diagnosing noise level issues in rooms due to HVAC, exterior noise, motor-induced and transformer-induced noise, noise from lighting ballasts and fixtures, etc. Figure 15 shows an example measurement of the noise radiation from a set of axial fans. These types of measurements help determine the cause of interferences in acoustical environments and provide documentation to enable adequate acoustical corrections to be made. Figure 15: Measurement of axial fan noise radiation; the spectrum peak is the blade-passage frequency. Noise Criterion Analysis In addition to basic spectrum measurements, SmaartLive contains the capability to perform standard Noise Criterion, or NC measurements of continuous, broadband noise sources in rooms. Noise criterion measurement utilize a family of NC Curves which define thresholds for specifying the broadband noise level of a room (see Figure 16). Each curve is designated with a single number, such as NC-30 or NC-50. NC rating of the environment is derived from the maximum octave-band sound pressure level that meets an NC curve (or an interpolated curve inbetween primary curves). Figure 16: NC noise measurement; room is rated NC-57. The shape of the NC curves was originally developed relative to the level of annoyance of HVAC noise levels in rooms, but has since been accepted as a standard for quantifying many broadband noise sources. You will note that the NC curves are much higher in SPL at low frequencies; this is due to the equal-loudness contours of human hearing, given that the human ear is less sensitive to low frequencies. An important point to note is that NC ratings are not intended to be used when tonal noise is present; this means that the NC rating of a room is only significant when the source of the noise is mostly broadband, such as noise from air diffusers, etc. Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 13

78 Cinema System Certification An application that commonly requires an RTA for measurement is the certification of cinema and home theater systems to industry standards. While it is recommended that high-resolution equalization and loudspeaker setup tasks be performed with SmaartLive s Transfer Function and Impulse Response modes, most cinema standards groups require an RTA-based (usually 1/3 rd -octave) measurement for certification. This section will not cover the specific standards, but will review specific capabilities in SmaartLive for performing these measurements. Timed Spectral Averaging SmaartLive contains a Timed Spectral Averaging mode that allows for long-term acquisition of average spectra present in the environment. This mode is accessed by clicking on the SPL meter display and then clicking on the Timed Average / LEQ Setup button. As with L EQ measurements, you may select any observation period for the measurement. The result of this acquisition process is placed into a user-defined reference register. Because of the potential for a very long integration time, Timed Spectral Averaging is valuable for obtaining highly stable measurement results with random noise sources, such as the use of pink noise during an equalization process or for quantifying broadband room noise. Verifying Filter Calibration Typical large-format cinema systems utilize the ANSI/SMTPE 202M X-curve for equalization of the main loudspeaker system. The X-curve, shown in Figure 17, provides a uniform 3 db/octave high frequency rolloff beyond 2 khz, and a (somewhat less important) low-frequency 3 db/octave rolloff below 63 Hz. When a cinema system in a large room is equalized to this specification, less high frequency energy will reach the listeners, which has been found to be more audibly-pleasing than a flat response when the listeners are seated at a distance from the loudspeaker system. When certifying these systems for cinema use, the Inverse X-curve may be activated under the Weight spinner for the RTA. Now, with pink noise excitation, a loudspeaker system correctly conforming to the X-curve will display a flat 1/3 rd -octave spectrum in the RTA display. 5 0 Magnitude (db) Frequency (Hz) Figure 17: ANSI/SMTPE 202M X-curve. Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 14

79 Spatial Averaging In many cinema standards, spatial averaging of measured spectra is required in order to verify that the correct performance is obtained across the entire audience area. SmaartLive simplifies this task using Reference Trace Averaging, which allows several measurements to be performed at different seating positions and then power-averaged to produce an overall performance curve. In order to average up to four reference traces, capture each measurement into a separate reference bank (i.e., A1, B1, C1, and D1). The E bank is used to hold the average; activate the E register, press the button, and the press the button. The averaged curve will appear on screen with the original reference curves (Figure 18). Figure 18: Spatial averaging of 1/3 rd -octave RTA measurements using the averaging buffers. Gray curves: individual measurements, Red curve: spatial average. Suggestions for Further Reading D. Davis, C. Davis: Sound System Engineering, 2 nd edition. Carmel, IN: SAMS M. Mehta, J. Johnson, C. Rocafort: Architectural Acoustics: Principles and Design. Upper Saddle River, NJ: Prentice Hall American National Standard: Specification for Sound Level Meters, ANSI S New York, NY: Acoustical Society of America R. Cabot, B. Hofer, R. Metzler: Standard Handbook of Video and Television Engineering: Chapter 13.3: Nonlinear Audio Distortion, 4 th edition. McGraw-Hill Professional OSHA Standard: Occupational Noise Exposure, OSHA Washington, DC: Occupational Safety & Health Administration Criteria for a Recommended Standard Occupational Noise Exposure, Revised Criteria 1996, DHHS (NIOSH) Publication No. 96. Atlanta, GA: National Institute for Occupational Safety & Health Motion-Pictures - B-Chain Electroacoustic Response - Dubbing Theaters, Review Rooms and Indoor Theaters, SMPTE 202M White Plains, NY: Society of Motion Picture and Television Engineers Spectrum-Mode Measurements with SmaartLive: Concepts and Applications Page 15

80 NOTES

81 SIA-Smaart Application Notes Loudspeaker Impedance Measurements with SmaartLive Presented by: SIA Software Company, Inc A LOUD Technologies, Inc. Company

82 Copyright SIA Software Company, Inc. A LOUD Technologies, Inc. Company All rights reserved

83 LOUDSPEAKER IMPEDANCE WITH SIA SMAARTLIVE SIA SmaartLive Technical Note Paul D. Henderson Program in Architectural Acoustics, Rensselaer Polytechnic Institute, Troy, NY A recent addition to the capability of SIA SmaartLive is the ability to measure complex load impedance as a function of frequency. The potential to perform these measurements permits investigations of loudspeaker behavior in the field with accuracy previously available only in the laboratories of loudspeaker manufacturers. This tool may be used to troubleshoot loudspeaker drivers, systems, and constant voltage networks, as well as to design related systems and select optimal loading conditions for power amplifiers. This article provides an overview of the measurement technique and necessary theory for taking advantage of this useful tool. 1. AN INTRODUCTION TO LOUDSPEAKER IMPEDANCE The term impedance is widely used in the professional audio industry, but frequently misunderstood and misapplied. Impedance is the total opposition to the flow of alternating current (AC current) in an electric circuit, and is a complex function of frequency as the ratio of voltage to current (Equation 1). The concept of impedance is analogous to resistance in direct-current (DC) circuits. While impedance includes resistance, it includes another element exclusive to AC circuits, reactance, which is due to the energy storage effects in AC circuits from components like inductors and capacitors, which vary as a function of frequency. In engineering circles, impedance is thought of as a complex quantity, meaning it includes both real (resistive) and imaginary (reactive) parts (Equation 2). It is this concept that accounts for the varying phase shift of impedance: current flows through resistive components in phase with the applied voltage, while current flows through reactive V( f ) Z ( f ) = I( f ) (Eq. 1) Z ( f ) = R( f ) + j X( f ) (Eq.2) 2 2 Z( f ) = Z ( f ) = R ( f ) + X ( f ) (Eq.3) components with a phase shift relative to the applied voltage. The impedance magnitude (Equation 3) contains the effects of both the resistive and reactive components, and indicates the total opposition to current in the circuit (ignoring phase). It is this magnitude function that is typically quoted in loudspeaker specifications, as it is the impedance magnitude that affects the total current required from an amplifier when driving the loudspeaker. While the above V Figure 1: Z I general concept of impedance is universally used in many circuit analysis tasks, the concept of load impedance or the input impedance of a load (such as a loudspeaker) seen by a driving source (such as a power amplifier) is what we typically deal with when looking at loudspeaker characteristics (see Figure 1). The electrical input impedance function of a real loudspeaker is defined by many factors, including electrical, mechanical, and acoustical behavior. Electrically, the resistance and inductance of the voice coil dominates, along with the presence of any passive crossover components. The mechanical mass, compliance ( springy-ness ), and resistance of the drivers form another component of the total impedance. Additionally, the acoustical impedance seen by the drivers appears as part of the electrical impedance function, including the baffle loading effects, any loudspeaker ports, etc. All of these factors combine to create the impedance functions seen by measuring a typical loudspeaker.

84 Loudspeaker Impedance with Smaart Figure 2 shows the impedance magnitude-versus-frequency curve for a single low-frequency driver in both a sealed and ported enclosure. The strong dependence of impedance on frequency is easily seen. In the sealed example, the peak is created by the resonance between mechanical compliance and mass in the driver. The second peak appearing in the ported case is the acoustical tuning resonance of the vent. The rise in impedance at high frequencies is due to the inductance of the voice coil, while the minimum value of the graph is equal to the resistance of the voice coil. These characteristics are typical examples of measured data from real loudspeaker systems, providing vital information about the loudspeaker system for troubleshooting and design. The included bibliography lists several excellent references for interpreting and applying this information. Figure 2: Input impedance of a single low-frequency driver in both a sealed and ported enclosure. 2. IMPEDANCE MEASUREMENT TECHNIQUES Using the concepts developed in Section 1, we can now investigate methods of measuring load impedance. Based on Figure 1, we can see that the load impedance function may be obtained directly if we are able to acquire signals representing both the voltage and the current into the load impedance over all frequencies of interest. Since computer sound cards respond to voltage signals, a signal proportional to the voltage across the load is easily acquired by simply feeding the load voltage directly to the sound card. However, other techniques must be used to acquire the current signal. The current signal is most easily measured by inserting a shunt resistor in series with the load, creating a current shunt; the current in the load is then directly I R shunt proportional to the voltage across this shunt resistance (see Figure 3). This is the method employed by most digital multimeters on the market to measure current. There are other methods of deriving the current signal, including the use of inductive current probes, etc., Z V however, the shunt resistance method is the most practical technique for measuring loudspeaker impedance with SmaartLive. As outlined above, if the voltage across the shunt Figure 3: Impedance measurement with a shunt resistor. resistance is measured, the current may be derived. However, if the source in Figure 3 is ground-referenced, the shunt resistor voltage is floating, so a differential amplifier must be used to directly measure this voltage. Using SmaartLive, the circuit required to use this differential (balanced) measurement technique is shown in Figure 4. The differential inputs may be provided using anything from a laboratory-grade differential amplifier to a balanced line-level input on a professional audio interface or mixer. However, for Smaart users desiring a simpler interface or lacking a differential input, a single-ended (unbalanced) measurement technique is possible, with SmaartLive calculating the exact load current internally. Both techniques have advantages and disadvantages, along with trade-offs associated with the selection of the value of the shunt resistor. Page 2 of 7

85 Loudspeaker Impedance with Smaart Figure 4: Smaart impedance measurement circuit with a differential (balanced) input technique. Figure 5: Smaart impedance measurement circuit with a singleended (unbalanced) input technique. Table 1 compares the two measurement techniques, presenting the trade-offs associated with each. In general, for a laboratory-grade measurement solution, choose the differential method with a highgrade balanced-input preamplifier. If you desire a simple, practical solution, choose the single-ended method, being certain to adequately calibrate your measurement system appropriately. SmaartLive requires you to use a calibration resistor to calibrate the measurement configuration based on this reference resistance for maximum accuracy. This calibration resistance temporarily replaces the load impedance during the calibration routine, which will be reviewed later. Differential Method Advantages: High-accuracy, large-range with low noise differential amplifiers Insensitive to differences in input channel gains; simple calibration Disadvantages: Complex input circuitry required Single-Ended Method Advantages: Simple, passive design No common-mode considerations Disadvantages: Sensitive to mismatch in input channel gains; requires careful calibration Table 1: Comparison of impedance measurement methods. 3. OPTIMIZING THE MEASUREMENT HARDWARE Before you jump in and start making impedance measurements, you should be aware of the practical issues involved in building an impedance measurement circuit and interfacing this device with your computer. Selecting appropriate shunt and calibration resistors will affect the quality of your measurements, and care must be taken when interfacing the computer with loudspeaker-level signals. Driving the Circuit Just like transfer function and impulse response measurements in SmaartLive, the impedance measurement function is dependent on a broadband excitation signal, such as random noise or a sinusoidal sweep, to perform its measurement. While transfer function measurements will use this signal to drive input of the device under test, the impedance function uses this signal to excite the load through the current shunt. When a dynamic loudspeaker is driven by a source with relatively high source impedance (like a current shunt), the effect of the loudspeaker acting in reverse as a microphone may affect the quality of your measurements if there is sufficient acoustic noise in the measurement room. In order to minimize this problem in situations with a high ambient noise level (such as a construction site, manufacturing floor, etc.), the shunt resistance must be relatively small, and a small power amplifier used to drive the circuit. This, however, must be carefully undertaken in order to avoid damage to Page 3 of 7

86 Loudspeaker Impedance with Smaart your computer hardware. Power amplifier signals can easily exceed the maximum input voltage capability of conventional computer sound cards, and the power handling capability of the shunt resistor becomes increasingly important as more current is drawn into the load. When using a power amplifier, the output voltage must be limited to a safe level and power resistors used in designing the current shunt. In situations where ambient noise is not a concern (closed sites, laboratories, etc.), the headphone amplifier of the sound card may be safely used as the excitation source. Headphone amplifiers are typically rated for load impedances greater than ~30Ω, so the shunt resistance should be at least equal to this value. For typical loudspeaker loads, this shunt resistance limitation does not pose any question of accuracy to the measurement as long as ambient acoustic noise levels are minimal. Selecting Resistors The value, precision, and power handling capability of the resistances should be optimized when configuring the circuit based on the measurement conditions and load. Selecting an appropriate shunt resistance allows you to optimize the signal-to-noise ratio of the measurement while best taking advantage of the dynamic range and resolution of the system. Conversely, the calibration resistor should be of high precision and on the same order of magnitude as the unknown load impedance for maximum accuracy. For designs using a power amplifier, 2%-tolerance non-inductive wire wound resistors may be safely used, which are readily available with power ratings 10W. In current shunt designs where a headphone amplifier is used, 1%-tolerance metal-film resistors may be selected, which are obtainable with power ratings from ¼W-2W. The value of the shunt resistance should be selected based on the limitations of the driving amplifier and the approximate expected value of the load. Selecting too low a resistance here may draw too much current from the driving amplifier, overheating the resistor or distorting the amplifier. Too high a resistance may cause the voltage drop across the load to become negligible compared to crosstalk, calibration errors, etc., producing inaccurate results. In general, the shunt resistance should be comparable to the expected load resistance and no less than the minimum load impedance for the driving amplifier, with the calibration resistor in the same range. For example, when testing 4-16Ω (nominal) loudspeakers with a headphone amplifier, selecting a 50Ω shunt resistor and a 20Ω calibration resistor is a reasonable choice. However, when testing a 10Ω /70V constant-voltage line, a 500Ω shunt resistor is probably better suited to the task. Table 2 shows suggested values for the shunt resistor when testing various loads using both a small power amplifier and a typical headphone amplifier as the driving source. Load R shunt Power Amplifier R shunt Headphone Amplifier 4-16Ω loudspeaker 8Ω 50Ω 100Ω /140V line 200Ω 200Ω 10Ω /70V line 500Ω 500Ω Note: The value of R shunt should never be less than the suggested load impedance for the driving amplifier. Table 2: Suggested shunt resistances for various loads driven by typical amplifier configurations. When measuring high impedance loads, the input impedance of the sound card becomes significant to the measurement, rendering the calculation mathematics ineffective. In general, load impedances greater than 1/10 th of the sound card input impedance should not be measured. For loads in this range, use a quality high-impedance buffer amplifier. Page 4 of 7

87 The power dissipation rating for the shunt resistor should be at least equal to the value calculated by Equation 4. For most standard loudspeaker measurements using a headphone amplifier as the driving source, a ½W resistor is acceptable. More attention must be given to this parameter when using a power amplifier. For example, a power amplifier sourcing 2V RMS on its output into a 4Ω shunt resistance will require a shunt resistor rating of at least 1W Loudspeaker Impedance with Smaart P rating V R srcmax shunt 2 (Eq. 4) Power rating for shunt resistors. V srcmax is the maximum RMS output voltage of the driving amplifier. (continuous). Following the above guidelines will help ensure that your impedance measurements are of the maximum accuracy possible, and that the possibility of overheating components or damaging hardware is minimized. 4. USING THE SMAARTLIVE IMPEDANCE FUNCTION Building on the preceding review of the Smaart impedance measurement technique and the guidelines for configuring an impedance measurement circuit, this section will take you through a complete impedance measurement using SmaartLive. The desired measurement will be the load impedance of a small 5Ω (nominal) 2-way nearfield loudspeaker. Step 1: Connect the Measurement Circuit Based on the recommendations in Section 3, this measurement will be performed using the headphone amplifier of the computer sound card. Since the measurement is of a low-impedance loudspeaker, a 50Ω shunt resistor will be used, which is within the load capability of the headphone amplifier, and is reasonable to optimize the dynamic range of the measurement. Either the singleended (Figure 4) or differential (Figure 5) technique may be used to measure the load impedance; their results are identical assuming the system is correctly calibrated. In either case, the loudspeaker and calibration resistors are substituted for the unknown impedance Z in the schematics. Step 2: Configure SmaartLive The preparation in SmaartLive for running an impedance measurement is similar to that for a transfer function measurement. The generator must be configured and gains adjusted to eliminate input clipping. Open SmaartLive and enter transfer function measurement mode. Turn on the generator, typically for a synchronized sine-sweep signal. The standard FFT size versus frequency resolution trade-offs exist as with standard transfer function measurements. For this example, a 32K-bin FFT is selected, as measurement time and update speed are not a significant consideration. Disconnect any load from the circuit, and set the generator level to provide a signal level close to clipping on the Smaart measurement input. At no time after connecting a load will a signal exceed this level (Figure 6a). If you are utilizing the single-ended measurement technique, you must match the input gains for the two input channels using the sound card gain controls, the mixer balance control, etc. If you are using the differential technique, you may skip this step; the mathematics of the differential method automatically compensate for differences in channel gains. To perform the calibration, disconnect any load from the circuit and adjust the gain controls until the two channel levels are equal (Figure 6b). This may also be easily and somewhat more accurately accomplished by looking at the (logarithmic) transfer function magnitude and adjusting the controls until the curve reaches 0dB across the spectrum. Figure 6: (a) Adjust signal levels to eliminate clipping; (b) Match channel levels in single-ended mode. Page 5 of 7

88 Loudspeaker Impedance with Smaart After performing these adjustments, the impedance mode may be launched by selecting Lin (linear) on the Transfer Function > Amplitude Scale menu (Figure 7). Figure 7: Launching impedance mode. Step 3: Calibrate with a Reference Resistor Now that the impedance mode has been launched and the signal levels adjusted, connect the calibration resistor (discussed in Section 3) in place of the load. Double-click on the plot area, launching the calibration dialog box (Figure 8). Select the appropriate circuit topology (in this case, single-ended) and enter the value of the calibration resistor (not the shunt resistor) into the Calibrated Impedance is edit box. In this example, we ll enter 49.9Ω, which was measured with a precision ohmmeter. Click OK to finalize the calibration. Step 4: Perform the Impedance Measurement After calibrating the system, the measurement shown on the display reflects the impedance of the calibration resistor, which, in this case, is a constant 49.9Ω (Figure 9). Now, the loudspeaker may be connected as the load, and the actual unknown load impedance measured. For this example, the resulting impedance magnitude measurement is shown in Figure 10. Figure 8: Impedance calibration dialog box. For this 2-way system, the mechanical resonance of the lowfrequency driver is easily seen at approximately 90Hz, as well as the high-frequency peak created by the passive crossover network. One item to note: this loudspeaker is rated as having 5Ω nominal impedance, but the minimum Figure 9: Measurement of the calibration resistor. value in the audio bandpass is only 3.9Ω. This information might influence decisions on how many devices to place on a single amplifier channel, etc. In more advanced applications, these impedance measurement results may yield Thiele-Small parameters for single drivers or other design information. This example demonstrates the accuracy and potential value of the impedance measurement capability in SIA SmaartLive. Page 6 of 7