UNIVERSITY OF MIAMI ADAPTIVE ROOM CORRECTION AND CROSSOVER CALCULATION FOR ENHANCED SATELLITE-SUBWOOFER INTEGRATION. Rian Wayne Chung A THESIS

Transcription

1 UNIVERSITY OF MIAMI ADAPTIVE ROOM CORRECTION AND CROSSOVER CALCULATION FOR ENHANCED SATELLITE-SUBWOOFER INTEGRATION By Rian Wayne Chung A THESIS Submitted to the Faculty of the University of Miami in partial fulfillment of the requirements for the degree of Master of Science Coral Gables, Florida May 2006

2 UNIVERSITY OF MIAMI A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science ADAPTIVE ROOM CORRECTION AND CROSSOVER CALCULATION FOR ENHANCED SATELLITE-SUBWOOFER INTEGRATION Rian Wayne Chung Approved: Colby Leider Professor of Music Engineering Dr. Edward Asmus Associate Dean, Graduate Studies School of Music Ken Pohlmann Director of Music Engineering Dr. James Shelley Director of Audio Engineering

3 CHUNG, RIAN W. (M.S., Music Engineering) Adaptive Room Correction and Crossover (May 2006) Calculation for Enhanced Satellite-Subwoofer Integration Abstract of a thesis at the University of Miami. Thesis supervised by Professor Colby Leider. 109 pages. (102) This paper describes a method to measure and calculate filters for room equalization and crossovers. This method was designed to be easy for the user to set up and use. An adaptive filter was used for the room equalization and crossover selection. During the setup of the filters, the system equalizes for a known crossover frequency, and then it changes the crossover frequency and repeats the equalization again. After all of the equalizing filters for each of the available crossover frequencies are computed, the optimized crossover will be selected based on the sum of the absolute value of the gain and attenuation of the equalizing filter.

4 Table of Contents Table of Figures... v 1 Background Sound Reproduction Speaker Design Speaker Enclosure Crossovers Active Versus Passive Crossovers Subwoofers Satellite Subwoofer Systems Listening Environment Specular Reflection Diffuse Reflection Standing Waves Absorption Room Equalization Digital Signal Processing Adaptive Filters Wiener Filters Method of Steepest Descent Least-Mean-Square Algorithm Impulse Response Measurement Problem Definition Physical Size Aesthetics Low-Frequency Reproduction Room Effects Digital Room Correction Parametric Equalization Tuning Ease of use Test Signals Proposed solution System Components Main Speakers Subwoofer Digital Signal Processor Measurement White Noise Microphone Digital Crossover Adaptive Filter Implementation The Setup Main Speakers Subwoofer iii

5 4.1.3 Combined The Rest of the System Adaptation Simulation Speakers Room Crossover Microphone Transport Results Ideal High-Pass Ideal Low-Pass Ideal Combined Ideal Simulated Simulated High-Pass Simulated Low-Pass Simulated Combined Crossover Selection Simulated Adaptation High Frequency Speaker Conclusion Problems with the Simulation Results Real World Implementation Further study References iv

6 Table of Figures Figure 1: Sealed loudspeaker enclosure system... 3 Figure 2: Vented enclosure system... 3 Figure 3: Crossover Example... 5 Figure 4: Acoustimass 5 Satellite Subwoofer Speakers (image courtesy of Bose) Figure 5: Specular reflection... 9 Figure 6: Diffuse reflection Figure 7: Example of an absorbtion Figure 8: Digital Room Correction Impulse [36] Figure 9: Digital Room Correction Frequency Response [36] Figure 10: Signal Flow Diagram Figure 11: DSP Processing in blue Figure 12: White Noise Power Spectral Density Figure 13: Common Adaptive Filter Block Diagram for Channel Equalization Figure 14: System block diagram Figure 15: Athena Audition AS-B1 Frequency Response Figure 16: Celestion S20 Low Frequency Response Figure 17: Combined speakers and subwoofer frequency response Figure 18: Measurement System Setup Figure 19: Simulated Main Speaker FIR Filter Figure 20: Simulated Subwoofer FIR Filter Figure 21: Low Pass Filter Figure 22: High Pass Filter Figure 23: Combined Crossover Figure 24: Simulated microphone Figure 25: Simulated transport Figure 26: Frequency Response of Ideal Noise Figure 27: Ideal High-Pass Processing Block Diagram Figure 28: Ideal High-Pass Filtered Noise Figure 29: Ideal Low Pass Processing Block Diagram Figure 30: Ideal Low Pass Filtered Noise Figure 31: Combined Ideal Filters Figure 32: Simulated High Pass Block Diagram Figure 33: Simulated High Pass Room and Speaker Response Figure 34: Simulated Low Pass Block Diagram Figure 35: Simulated Low Pass Room and Speaker Response Figure 36: Simulated Combined Room and Speaker Response Figure 37: Gain/Reduction of equalizing filter Figure 38: Simulated real response with 80 Hz crossover Figure 39: Last corrective filter 80 Hz Figure 40: Simulated corrected response with 80 Hz crossover Figure 41: Error plot 80 Hz crossover Figure 42: Actual Response with last Adaptation Coefficients (80 Hz Crossover) Figure 43: Simulated real response with 90 Hz crossover Figure 44: Last corrective filter 90 Hz Figure 45: Simulated corrected response with 90 Hz crossover v

7 Figure 46: Error plot 90 Hz crossover Figure 47: Actual Response with last Adaptation Coefficients (90 Hz Crossover) Figure 48: Simulated real response with 100 Hz crossover Figure 49: Last corrective filter 100 Hz Figure 50: Simulated corrected response with 100 Hz crossover Figure 51: Error plot 100 Hz crossover Figure 52: Actual Response with last Adaptation Coefficients (100 Hz Crossover) Figure 53: Simulated real response with 110 Hz crossover Figure 54: Last corrective filter 110 Hz Figure 55: Simulated corrected response with 110 Hz crossover Figure 56: Error plot 110 Hz crossover Figure 57: Actual Response with last Adaptation Coefficients (110 Hz Crossover) Figure 58: Simulated real response with 120 Hz crossover Figure 59: Last corrective filter 120 Hz Figure 60: Simulated corrected response with 120 Hz crossover Figure 61: Error plot 120 Hz crossover Figure 62: Actual Response with last Adaptation Coefficients (120 Hz Crossover) Figure 63: Simulated real response with 130 Hz crossover Figure 64: Last corrective filter 130 Hz Figure 65: Simulated corrected response with 130 Hz crossover Figure 66: Error plot 130 Hz crossover Figure 67: Actual Response with last Adaptation Coefficients (130 Hz Crossover) Figure 68: Standard deviation of the results Figure 69: Peak-to-peak values Figure 70: Cambridge Soundworks DTT2500 speaker frequency response Figure 71: Cambridge Soundworks speakers and the subwoofer no equalization or crossover Figure 72: Gain/Reduction of equalizing filter Figure 73: Equalized with 150 Hz crossover and non-equalized Cambridge Soundworks speakers vi

8 1 Background 1.1 Sound Reproduction Sound reproduction is the process of recreating the prerecorded sound in the way the artist had originally intended the sound to be heard. In home listening environments, typically the sound reproduction chain consists of a CD/DVD player, receiver, speakers, and the room. It is the goal of this chain of equipment to be transparent. Transparency, in the terms of audio fidelity, typically means no change in the audio signal from the recording studio to the ears of the listener. Of these, the room and the speakers tend to have the most variations and difficulty in reproducing a flat frequency response Speaker Design Speakers are a subjective part of the audio reproduction chain. The ideal speaker would be efficient, have a flat frequency and phase response, and be invisible. Since this is not possible due to physics, designers must make compromises to create a system to meet or exceed the user s expectations on all three fronts. Transducers are usually placed in enclosures to improve the frequency response. As in the case of vented enclosures, certain frequencies are boosted. Other techniques to improve the frequency response of the speaker use electrical systems that modify the frequencies of the signal before the signal is converted into mechanical energy [2],[3],[4], [7]. These modifications can take place in either or both the digital and analog domains. 1

9 Speaker Enclosure The main purpose of a speaker enclosure is to act as a baffle to prevent the backward propagation of the wave from canceling the forward propagation of the wave. This cancellation is more of a problem for low-frequency waves than high-frequency waves, because of the way the low-frequency wave propagates. Low-frequency waves propagate in an omni-directional spherical fashion that produces waves in both the forward and reverse direction. There are a variety of different enclosures that are in use, but the most commonly used enclosures are sealed and bass reflex which are also referred to as vented enclosures. The different enclosures are another way to affect the frequency response of the system. Sealed The sealed enclosure is one of the simplest enclosures to design and build. In a sealed enclosure, the backward propagating waves are isolated from the front-propagating waves. When sealing a box, standing waves inside the box can become a problem. For that reason, acoustical absorbing material is sometimes added to the inside. With the added absorption, it will take the wave longer to reach the rear of the box making the box seem larger. An example of a sealed enclosure is shown in Figure 1. V AB is the effective volume of air in the box including the filling effect.

10 3 Driver V AB Enclosure Figure 1: Sealed loudspeaker enclosure system. Vented Vented loudspeakers contain a small port in a sealed enclosure. The vent in the enclosure is modeled as an acoustic mass, which when combined with the compliance of the air in the enclosure form a Helmholtz resonator. The resonance frequency of the Helmholtz resonator will give this system a boost at that resonance frequency. An example of a vented enclosure is shown in Figure 2. Driver V AB Enclosure Vent Figure 2: Vented enclosure system Crossovers A typical single speaker driver is unable to reproduce the entire audible spectrum, 20 Hz 20 khz, without significant amounts of distortion. It is common practice to use multiple drivers to accomplish such a task with a frequency-dividing network. This dividing network prevents frequencies the driver is unable to produce from being seen by that driver. These frequency-dividing networks are called crossovers, but they are really

11 4 just basic filters. Crossovers can also help with the frequency response of the speaker if needed by giving a boost or reduction to certain frequencies. Most common loudspeakers contain two or three drivers consisting of a high-frequency network, a low-frequency network, and sometimes a mid-range network. A subwoofer in these systems is used to extend the bandwidth of the sound reproduction system to lower frequencies. Satellite subwoofer systems use crossovers to send mid-high frequencies to the satellite speakers and the low frequencies to the subwoofer. At the same time, it is the subwoofer s responsibility to reproduce what would normally have been taken care of by the low-frequency driver of the speaker Active Versus Passive Crossovers Crossovers can be active or passive [30]. Active crossovers are placed before the signal is amplified and filtered at line-level. Figure 3 shows an example of an active crossover network. Passive crossovers are built into the speakers and consist of only passive components. Active crossovers have many benefits over passive crossovers. Amplifiers, when driving passive networks, are faced with complex impedances that can be inefficient and cause signal distortion. In particular, the inductors on the low-frequency network can cause non-linearities due to quality of materials. By placing the crossover before the amplifier, the high-frequency signals are isolated from the low-frequency signals, and the low-pass network can be built with only resistors and capacitors.

12 5 Passive Crossover High High-Pass Filter Power Amplifier Passive Crossover Signal Source Mid Low-Pass Filter Power Amplifier Low Figure 3: Crossover Example. Subwoofers and satellite speakers are normally driven by separate amplifiers. By driving the system with separate amplifiers, the active crossover can be obtained. If one speaker and subwoofer were considered separately, a high-pass crossover placed between the signal and the amplifier going to the satellite speakers would create a bi-amped active system. A system that is set up with satellite speakers shares their low-frequency signals from the left and right channel with the subwoofer. which relies on the omni-directional nature of low-frequency waves Subwoofers A specialized speaker, called a subwoofer, is used to reproduce the lowest part of the audio spectrum. A subwoofer can generally reproduce signals with acceptable distortion from 80 Hz down to 20 Hz.

13 6 Subwoofer Blending Blending a subwoofer into the system is the processes of adjusting the crossover and the gain on the subwoofer to match the cutoff frequency of the main speakers. It is important for the system to be blended properly for the accurate reproduction of the sound. The blending process must also take into account the effect the room has on the sound, which is different for every room. A blended subwoofer will have a low-pass crossover frequency equal to the high-pass crossover of the speaker and the volume level of the subwoofer will be equal to the speaker s volume level. When properly blended, the speaker system should sound like a pair of large speakers. If the speakers have been improperly set up, a hole or a large gain in the frequency response could exist, depending on the overlap. The level of the subwoofer should match the level of the speakers. Subwoofer Placement It was stated earlier that, since the subwoofer reproduces low-frequency sound waves, the placement of the subwoofer theoretically could be anywhere. In practice, room boundaries affect the sound that is reproduced by the subwoofer. Standing waves and reflections of the room all affect the sound. If a subwoofer is placed in a position in a room where low-frequencies resonate, room correction should be applied to tame these frequencies.

14 Satellite Subwoofer Systems A type of speaker system called a satellite subwoofer system was made popular by Bose with their Acoustimass speakers in When typically demonstrated in a retail stereo shop, the small cube speakers would be hidden behind much larger speakers. After the demonstration was done, it was revealed to the listener that they were listening to small 4 x 6 speakers. The trick to the system was the use of a passive subwoofer reproducing the lower frequencies and being placed out of the way. An image of the Bose Acoustimass 5 speaker system is shown in Figure 4. Figure 4: Acoustimass 5 Satellite Subwoofer Speakers (image courtesy of Bose). Subwoofer satellite combination systems, despite their limited audio fidelity, have made themselves common in living room home theater setups. Some reasons for their popularity include the price of the system and the size of the speakers making them easily

15 8 placed in a room. Due to the physical size of these satellite speakers, they are unable to produce low-frequency sounds. Therefore they must be coupled with a subwoofer for the reproduction of the lower-frequency waves [3]. Low frequencies from each channel are combined and sent to the subwoofer. A subwoofer, in theory, produces low-frequency sound that psychoacoustically the direction cannot be localized well. The placement of the subwoofer therefore is not all that difficult, even though it has a larger size than the satellite speakers, since it can be placed theoretically anywhere in the room. Since most users do not have a dedicated listening room, placing large speakers that are capable of reproducing the entire audio spectrum is often not possible. The small speakers and large go anywhere subwoofer combination is very appealing to such users. Another advantage is the cost factor of such systems. In a multi-channel environment, only one woofer is used for typically five satellite speakers [34]. Such a system is much less expensive to make than a system with five full range speakers Listening Environment As stated earlier, most users of sound-reproduction equipment do not have the luxury of a dedicated sound room for their equipment. The room in which the speakers are placed can have an effect on the sound much the same way the speaker enclosure affects the sound. The room size and materials (upholstery, carpets, wood floors, etc.) can play a significant role in the reproduction of the sound.

16 9 A speaker, when placed in a rectangular room with six walls and three pairs of parallel surfaces, will display the effect of an infinite number of sources. The walls act analogously to sound like mirrors do to light. The walls are not perfect reflectors and therefore the signal will degrade through time. The amount of energy the wall absorbs can be changed by changing the material of the wall. Each type of material will absorb different frequencies differently Specular Reflection Specular acoustic reflections are the waves that are reflected off of a surface like a mirror reflects light. The reflected energy is some fraction of the initial wave and is always less than one. Reflected waves will continue to bounce around the room until the energy of the wave has dissipated. Waves that are reflected around the room interact with each other as well as the direct waves from the speakers. For example too many specular reflections in a room can make movie dialog unintelligible. In general, it is a good idea to apply some absorption to both high and low frequencies. An example of a specular reflection is shown in Figure 5. Figure 5 also shows the use of Snell s law; the angle of incidence is equal to the angle of reflection. θ Incident Wave θ Reflected Wave Figure 5: Specular reflection.

17 Diffuse Reflection In a diffuse reflection, the incident wave is reflected uniformly from the surface. When compared to the light wave analogy, diffuse reflections are like a light wave reflecting off of a matte surface. For materials to cause diffusion, they generally must have textured, non-uniform surfaces. A perfectly diffuse sound arrives at the listener at the same time from all directions at equal energies. An example of a diffuse reflection is shown in Figure 6. Incident Wave Reflected Waves Figure 6: Diffuse reflection Standing Waves Standing waves occur when similar waves traveling in opposite directions have the same peaking spot. In listening rooms, standing waves occur because some of the wave energy is reflected back toward the speaker and the reflections match up with the produced waves. Standing waves can be observed in physical media such as columns of air closed on each side.

18 Absorption When a sound wave hits a surface, some of the energy is absorbed. Material designed specifically for sound absorption is called acoustic material. The amount of energy absorbed by the material depends on the frequency of the wave. Acoustic material is used in professional installations to help control the reverberation of the room, as well as echoes, such as flutter echo. The more energy that is absorbed by the absorption surface, the less energy there is to be reflected. Absorbed energy is converted into heat. An example of an absorbed wave is shown in Figure 7. Absorbed Wave θ Incident Wave θ Reflected Wave Figure 7: Example of an absorbtion Room Equalization Every room is different and therefore every speaker sounds differently depending on the room. Smaller rooms play a particular role in low- frequency sounds where standing waves can be a problem. Low-frequencies have this effect in smaller rooms because of the length of the wave versus the size of the room. The room effect can be considered a transfer function on paper just like the crossover and the loudspeaker. When a signal is convolved with each of these devices, we get the sound that our ears hear. If the transfer function of the room were to be identified, an exact inverse transfer function placed in the

19 12 signal path would in theory nullify the room. When the transfer function of the room is identified; filters can be designed to almost invert the room response. The typical room environment is not minimum phase and therefore cannot be perfectly inverted. There are other problems such as when the frequency of a signal is raised, and the area that the correction covers is narrowed to the slightest movement of the head. Digital room correction is not just equalizing the peaks and valleys of a frequency response by adding or removing notch filters. In the digital room correction method, the user tells the system how they want the system to respond to signals and filters are designed to produce the response. Each speaker receives its own filter to compensate for placement differences in the room. The process of room equalization consists of three parts. The first step is to measure the impulse response of the room from the speakers at the preferred listening location. After the impulse response is determined, an inverse filter must be found. The inverse filter is then added to the signal path to provide the equalization. 1.2 Digital Signal Processing Digital signal processors are used to process digitally sampled data. In the digital domain, signals can be processed at a reduced cost due to rapid advancement of processing techniques. Consumer electronics are available that convert analog audio signals to the digital domain so that they can be processed inexpensively and at a higher quality than in the analog domain.

20 Adaptive Filters Adaptive filters are often used to identify unknown systems or signals and remove the noise from the signal. Adaptive equalization is used on communication lines to identify and eliminate noise as well as adjust for the non-linearity in the transmission line. The transfer function of the line is determined and an inverse transfer function is created by measuring the error. The popularity of adaptive filters is increasing for applications in noise control and echo cancellation due to the abundance of inexpensive DSP processors. These adaptive systems require the original signal, and an error signal, to identify the unknown transfer function. Adaptive filters build their own coefficients based on the desired output and the error. The adaptation time, error, and complexity of the filter, all vary with the type of adaptive filter used. The most popular type of adaptive filter used is the Least Means Squared algorithm (LMS) which is neither the best for error or convergence time, but it is computationally efficient. It is this computational efficiency and ease of use that makes the LMS filter the standard adaptive filter that is used. Recursive Least Square (RLS) and Kalman filters, which are starting to get more widespread use, require a lot of processing power, but tend to have better convergence and error. The convergence of the adaptive filter is the amount of time the adaptive filter takes to find the optimum filter solution to the problem. The optimum filter solution will be when the error of the filter, defined to be the desired signal minus the predicted signal, is no longer decreasing.

21 14 Adaptive filter use in high-fidelity sound reproduction has been limited Ronald Genereux, in his paper, described an adaptive filtering method to design filters for room correction [16]. The LMS algorithm was used to generate room correction filters. Joji Kuriyama and Yasuyuki Furukawa took adaptive room correction one step further by generating the filters during the playback of music [18] Wiener Filters The purpose of Wiener filters is to minimize the estimation error of a filter [6]. One way to minimize the estimation error is to optimize the filter to minimize the cost function. The cost function is a gradient of the error. As the gradient converges to a point the error converges to a minimum. The cost function that is commonly chosen in adaptive filtering is the mean-square error. By minimizing the cost function based on the meansquare value of the estimation error, traceable mathematics and a distinct minimum are available. The principle of orthogonality shows us that the mean-square cost function is k J = 2E[ u( n k) e *( n)] Equation 1 [6] The condition for minimizing the cost function is E[ u( n k) eo *( n)] = 0, k = 0,1,2,... Equation 2 [6] Using the principle of orthogonality, the minimum mean-square can be minimized. Wiener filters substitute in values for the minimization of the cost function as shown ( ) * ( ) E u n k d n woiu * ( n i) = 0, k i= 0 Multiplying the equation out we get = 0,1,2,..., Equation 3 [6] i= 0 w E[ u( n k) u *( n i)] = E[ u( n k) d *( n)], k oi = 0,1,2,..., Equation 4 [6]

22 15 Where E[ u( n k) u *( n i)] is the autocorrelation function of the input for a lag of i-k and E[ u( n k) d *( n)] is the cross-correlation between the filter input and the desired response for a lag of k. By using the vector p as the cross-correlation between the input vector and the desired response, and R as the autocorrelation matrix we can define the Wiener-Hopf equations for the optimized coefficients as 1 w o = R p Equation 5 [6] It is from the Wiener-Hopf equations that the gradient-based adaptation methods are derived from Method of Steepest Descent The method of steepest descent is a gradient-based adaptation method [6]. The method of steepest descent can be applied to the Wiener-Hopf equations to provide a time varying adaptation method to them. By operating on the true gradient vector, the method of steepest descent provides us with an accurate representation of the filter to be determined. Other gradient-based adaptation methods may offer similar accuracy but at most they will be close to the method of steepest descent since they are operating on an estimate of the gradient and not the real gradient. The equation for the method of steepest descent is as follows 1 w ( n + 1) = w( n) µ g w ( n) 2 Equation 6 [6] Where w is the vector of coefficients, g is the gradient of a mean squared error surface and µ is the step-size. The gradient vector is given by g w ( n) = J ( n) = 2p + 2Rw( n) Equation 7 [6] Then, by substituting for the gradient in Equation 6

23 16 w ( n + 1) = w( n) + µ [ p Rw( n)], n = 0,1,2,... Equation 8 [6] Where p is the cross-correlation vector between the input vector u(n) and the desired response d(n), and R is the correlation matrix of the input vector u(n). The method of steepest descent is recursive, and therefore constraints must be met in order to insure the stability of the system. There are two factors that affect the stability of the method of steepest descent, the step-size and the correlation matrix. To ensure stability, 2 0 < µ < Equation 9 [6] λmax Where λ max is the largest eigenvalue of the correlation matrix Least-Mean-Square Algorithm The Least-Mean-Square algorithm is a stochastic gradient algorithm; whereas the method of steepest descent is a deterministic gradient algorithm [6]. The difference between the two algorithms is that the LMS algorithm uses instantaneous estimates of the autocorrelation matrix R and the cross-correlation vector p, while the method of steepest descent uses the true values for autocorrelation R and the cross-correlation vector p. The basic LMS algorithm breaks down into two processes, the filtering process and the adaptation process. The adaptation process attempts to find the optimum coefficients for the filtering process using the estimated values in the autocorrelation matrix R and crosscorrelation vector p. The instantaneous estimations are referred to as R ^ ^ and p. ^ R ( n ) = u( n) u( n) ^ ( p n) = u( n) d *( n) h Equation 10 [6] Equation 11 [6]

24 17 Now by substituting in ^ R and of steepest descent, the LMS coefficients can be found ^ p into the gradient equation, as was done for the method ^ ^ w( n + 1) = w( n) + µ u( n)[ d *( n) u h ^ ( n) w( n)] This process is an iterative procedure that starts with ^ w(0) = 0 Equation 12[6] if prior coefficients are not known. The LMS algorithm can be applied to a deterministic environment and a nonstationary environment even though the method was derived from wide-sense stationary inputs. 1.4 Impulse Response Measurement Taking measurements of a room requires a microphone, loudspeaker, and test signal. Various test signals exist to find an impulse response of a room and loudspeaker. Log sine sweeps and Maximum Length Sequences (MLS) are two of the most popular and accurate impulse response measurement techniques. MLS testing signals, are a sequence of pseudo-random pulses. MLS measurements are used to get data on loudspeakers and room responses, and can even be used to find the absorption coefficient of materials. The MLS measurement technique has some advantages over other techniques, such as its high signal to noise ratio allowing for the impulse response to be generated even in noisy environments. Log sine sweeps are the other popular form of measuring a room and loudspeaker response. When using long (>5 seconds) sine sweep, the signal to noise ratio is very high

25 18 allowing for the computation of the impulse response in noisy environments. It has been said that the log sine sweep out performs the MLS measurement when assuming the system is non-linear [35].

26 2 Problem Definition 2.1 Physical Size The frequency range of the speaker is affected by the size of the box. If the box is too small, the speaker will exhibit a strong mid-bass without much low bass. This reality is why small speakers have trouble reproducing low frequencies Aesthetics When dealing with multipurpose rooms, such as a living room, speaker placement becomes difficult. Multi-channel sound reproduction environments require the placement of five to seven speakers. If the speakers are large, the ideal placement may be difficult or impossible. In addition, large speakers can negatively affect the room s decor Low-Frequency Reproduction If the low-frequency waves cannot be generated with the small speaker enclosure, an alternative method of reproducing the low-frequency sound must be found. Subwoofers are used to extend the low frequency response of standard speakers. Due to the nature of low frequency waves, our brain has trouble locating the source of the sound. A solution to a small speaker being only able to reproduce mid-range frequencies is to use a subwoofer to reproduce the lower frequencies. Since we cannot place the location of the sound, the subwoofer can theoretically be placed in any location. It has been shown 19

27 20 at Crystal Acoustics [24], that the subwoofer frequency can be raised from the THX standard of 80 Hz to 130 Hz by using digital room correction. 2.2 Room Effects Room shapes and objects in the rooms cannot be predicted for each user of a sound reproduction system. This problem of irregular rooms can be partially solved using digital signal processing. The two most common ways are using digital room correction and parametric equalization Digital Room Correction Digital room correction uses the impulse response of a room to tailor an appropriate filter to the room [36]. The filter is not limited by filter bands, like the parametric equalizer is, and in theory will produce a completely flat spectrum. Digital room correction filters have problems adjusting to changing environments. The amount of people in a room and their placement may be different during the playback of a recording than during the measurement of the room. This change can affect the ability of the digital room correction to produce a flat-frequency response. The figures below show the ability of digital room correction using standard FIR filters to correct for room conditions. Figure 8 and Figure 9 show an example of a DRC corrected room and speakers. Visually from Figure 9, it can be seen that the digitally corrected system has fewer peaks and valleys, as well as a smaller peek-to-peek amplitude.

28 Figure 8: Digital Room Correction Impulse [36]. 21

29 22 Figure 9: Digital Room Correction Frequency Response [36] Parametric Equalization Parametric equalization attempts to use notch filters to equalize the frequency spectrum. These equalization systems are typically limited to six to ten channels. When a notch is adjusted, not only the frequency at the notch center is affected but the frequencies around the center are also adjusted. When parametric equalization is performed, detailed room measurements must be taken so that the notch frequencies do not negatively affect the frequency response.

30 Tuning Since every room is different, each system must be tuned before accurate sound reproduction is achieved. Without any prior knowledge of acoustics, the setup of a multispeaker system with room correction can be difficult. Room measurements must be taken with all of the room conditions in place including the listeners. Speaker systems with multiple amplifiers also have to be normalized so that no one speaker is louder than another Ease of use A problem facing all consumer electronics design is the ease of use of the system. When dissected, consumer electronics are very complicated devices that try to present a simple easy to use interface to the user. The complexity should be transparent. It can be assumed that the user will know little if anything about acoustics and will probably just want the best sound they can get. The placement of the subwoofer and the setting of the crossover is a process that requires acoustical room measurements and knowledge of how to read the results. Room equalization also presents a problem for the user. During the setup of the listening environment, it is required that all of the objects that are to be in place during the listening be in place during the testing. This requirement prevents the user from properly setting up the system before the listeners are seated.

31 Test Signals The test signals that are used to produce an accurate impulse response are not pleasant to the ears. These signals must be played at a relatively high volume level to get accurate results. Users do not like to listen to these test signals often, and it is an inconvenience to replay them each time the environment changes.

32 3 Proposed solution The proposed solution is to blend the system s ease of use with audio fidelity by using advanced digital signal processing techniques. At first, an audio system will be defined to meet the frequency constraints of the main speaker and subwoofer. A digital signal processing algorithm will then be defined to adjust for the conditions in the room and the specification of the speakers. The system also blends the subwoofer with the main speakers. The equalizing processing technique, adaptive filtering, will automatically create the room correction filter. While the adaptive filter will correct for imperfections in the frequency response, a crossover frequency will be adjusted between the ranges of 80 Hz to 130 Hz to find the best match of crossover frequency to flat frequency response. As stated earlier, audio reproduction is a subjective field. It is the goal of the project to normalize the sound levels and flatten the frequency response of the speakers. 3.1 System Components The proposed solution will use typical home audio reproduction equipment and combine them with advanced digital signal processing. The main speakers, the subwoofer and the digital signal processor are defined with specifications. The transport, amplifier and preamplifier are the general forms of each and will be defined to have a flat frequency response. The signal flow diagram is shown in Figure

33 26 Audio transport Pre Amplifier DSP Amplifier Amplifier Satellite Speaker Subwoofer Figure 10: Signal Flow Diagram Main Speakers The main speakers will be defined to be able to have an almost flat frequency response down to 120Hz. This response will allow speakers that are smaller than full range speakers to be used in the system. The speakers may be two-way with their own passive crossovers or one single speaker Subwoofer The subwoofer will be defined to be able to have an almost flat frequency response up to 140Hz. It is likely that the subwoofer will have its own active crossover and amplifier. If the subwoofer has its own crossover, it should be set to the highest setting to allow the digital signal processor to do the filtering Digital Signal Processor The digital signal processor in the proposed solution must have enough processing power and memory to compute all of the calculations in real time. The processor will need to

34 27 process the crossover, the adaptation process, and the adaptive filter. Figure 11 shows the DSP block diagram. HP Filter Satellite Speaker Noise Adaptive Correction - Error LP Filter Subwoofer Figure 11: DSP Processing in blue. 3.2 Measurement An initial measurement of the room s frequency response will be taken with white noise. The white noise sequence must be long enough for the filter to completely adapt. After the white noise has been played, the filter coefficients of the last state of adaptation will be used for the room equalization coefficients White Noise A white noise signal is defined to have an even power spectral density and a zero mean. White noise is used to calibrate adaptive filters because the noise is uncorrelated. Adaptive filters converge quicker with uncorrelated input. Figure 12 shows the flat power spectrum on white noise.

35 28 Figure 12: White Noise Power Spectral Density Microphone A measurement microphone will be used to record the output of the system, and determine the error of the system. The microphone is defined to have a flat frequency response from 20 Hz 20 khz. The placement of the microphone will be at the user s desired sweet spot. 3.3 Digital Crossover The crossover in the system will consist of two Finite Impulse Response (FIR) filters. These filters will be one high-pass for the main speaker and one low-pass for the subwoofer. The crossover of the filter will vary between 80 Hz and 130 Hz. This

36 29 crossover is to separate the signals being sent to the subwoofer and the signals being sent to the main speakers. To adjust the crossover setting, the results from the adaptive filter will be analyzed. To analyze the equalizing filters the sum of the absolute value of the filter is determined. The resulting sums are then compared at each crossover frequency and the lowest sum is chosen to be optimum. The smallest peaks and valleys are easiest to compensate for in the real world. An adaptive filter will be applied before the crossover for room correction. 3.4 Adaptive Filter The heart of the system is an adaptive filter for room correction. Adaptive filters can be used for system identification. In this case, the adaptive filter will be used to identify the room/loudspeaker combination system and reduce their effects on the sound. To help in the ease of use of the system, the adaptive filter s operation is automatic and requires no input from the user. Adaptive filters require an error signal to adapt properly. A microphone will be used to provide the error signal for the appropriate listening position. The adaptive filter is set up in a channel equalization mode. The desired signal d(n) is delayed and compared with the output of the adaptive filter y(n). The error signal e(n) is computed to be d(n) y(n) and returned to the adaptive filter. Figure 13 shows the most common way to set up a channel equalization circuit.

37 30 Delay d(n) Signal s(n) Channel a(n) Adaptive y(n) Filter - e(n) Figure 13: Common Adaptive Filter Block Diagram for Channel Equalization. The actual setup will model the speakers as the channels. A band-pass filter between the noise and the delay will be used so that the adaptive filter will not try to adjust for frequencies below 20 Hz and above 20 khz. HP Filter Delay LP Filter HP Filter Satellite Speaker d(n) Noise s(n) a(n) Adaptive Filter y(n) - Error LP Filter Subwoofer e(n) Figure 14: System block diagram.

38 4 Implementation The implementation of the proposed solution will be simulated. A software mathematics program, MATLAB, provides a great tool to simulate the problem. To test the proposed solution, real impulse responses will be taken of both the main speakers and the subwoofer. These impulses will be read into MATLAB and used as the system to be identified and inverted. The computer running the MATLAB software is an emachines T The Setup For the simulation to be accurate, some real world parts will need to be measured. The speakers and subwoofer are measured using ETF 5 acoustic measurement software by Acoustisoft. ETF 5 uses the MLS measurement technique to determine the impulse response Main Speakers The speakers that are used are Athena Audition AS-B1 bookshelf speakers. The frequency response of the speaker is shown in Figure 15. This impulse response figure represents a combination of the room and the speaker. 31

39 32 Figure 15: Athena Audition AS-B1 Frequency Response Subwoofer The subwoofer used is a Celestion S20. This is an 8 woofer with a built in crossover and amplifier. In order to get the full frequency response, the crossover is set to its highest setting at 140 Hz. The frequency response of the subwoofer is shown in Figure 16.

40 33 Figure 16: Celestion S20 Low Frequency Response Combined Figure 17 shows the impulse response of the combined system. Here, it is shown that the subwoofer and speakers are not properly blended with one another by the large low frequency boost.

41 34 Figure 17: Combined speakers and subwoofer frequency response The Rest of the System The other components in the reproduction chain are a Sony DA50ES receiver, Behringer UB802 mixer, Behringer ECM8000 room measurement microphone, and a Creative Labs Soundblaster Live. The processor is a Compaq sr1710nx running Linux. BruteFIR is the software program used to perform real time convolution on the signals. The high-pass, low-pass, and equalizing filters are run in BruteFIR with the last known adaptation filter coefficients. When taking measurements for the combined system without the equalizer or crossover, JACK is used to pass the signal directly to the speakers and subwoofer unfiltered. The actual measurements are taken using ETF5 with the Behringer ECM8000 microphone placed in the listening position. The listening position is about six feet from the main speakers. The ETF 5 measurements are relatively accurate, not absolutely

42 35 accurate. Therefore, the decibel level may not be correct on the graph but the relative decibel level will be. While the components are not ideal, for the sake of this paper it will be assumed that these components are ideal so that the focus is placed on the speakers and the room. The setup is shown in Figure 18. Behringer ECM8000 Behringer UB802 Creative Soundcard Processor Creative Soundcard Sony DA50ES Celestion Subwoofer Athena Speakers Figure 18: Measurement System Setup. 4.2 Adaptation The method of adaptation used was the basic LMS algorithm. The adaptive filter output of the adaptive filter is sent to the crossover, which is then sent to the respective speaker. Each adaptive filter has a desired signal which is equal to the delayed version of the input with a bandpass filter from 20Hz 20kHz. An adaptive filter length of 8193 taps was used to help correct for some of the lower frequencies. In order to maintain convergence, the step-size that was selected was 2 µ = where M = tap size [6]. When using an LMS M algorithm based on a mean-squared error steepest descent, this step-size formula will ensure convergence if the signal power is one. 4.3 Simulation MATLAB was used to simulate the filter calculations. The source code for the simulation is located in the appendix.

43 Speakers Using the actual impulse responses from the Athena speakers and the Celestion subwoofer the MATLAB program can simulate the response of the system with convolution. The impulse response for the main speaker was imported into the MATLAB program as a wave file and an FIR filter of taps was constructed. The impulse response for the subwoofer was imported into MATLAB as a wave file and an FIR filter of taps was constructed. The frequency responses of the filters for the speakers and the subwoofer are shown in Figure 19 and Figure 20. Figure 19: Simulated Main Speaker FIR Filter.

44 37 Figure 20: Simulated Subwoofer FIR Filter Room The impulse responses of the speakers and subwoofer were taken while located in the listening room. The above impulse will account for the room response as well as the speaker s response Crossover The crossovers that the system will adapt to will be a standard FIR filter designed using a Hamming window since the Hamming window is the default window in MATLAB. There will be 8192 points in the filters. The crossover point will vary between 80 Hz and

45 Hz. All of the filters are created in MATLAB with the FIR1 function. Figure 21, Figure 22, and Figure 23 show an example of a 120 Hz crossover. Figure 21: Low Pass Filter.

46 Figure 22: High Pass Filter. 39

47 40 Figure 23: Combined Crossover Microphone The microphone is simulated as an ideal microphone. The signal recorded is the combined output of the simulated speakers and subwoofer.

48 41 Satellite Speaker + Microphone Subwoofer Figure 24: Simulated microphone Transport The transport is simulated with the wavread() command. The wavread() function in MATLAB will read a wave file into memory normalized between -1 and 1. Digital wave files are sent directly to the digital signal processor. This path also eliminates the need for a pre-amplifier. wavread() Adaptive Input Figure 25: Simulated transport. 4.4 Results The simulated results are shown. Ideal results are from white noise input that never leaves the DSP. The simulated results are from the white noise input that goes through

49 42 the simulated speaker and room channel. Real inputs are also used to show how music will be corrected dynamically Ideal In the ideal process, the signal when filtered by its crossover (high or low-pass) should be reproduced at the same exact levels. The ideal noise is shown in Figure 26. The high and low-pass frequency responses are from the initial crossover frequency of 120 Hz. Figure 26: Frequency Response of Ideal Noise.

50 High-Pass Ideal The high-pass ideal circuit is shown in Figure 27, and Figure 28 shows the frequency envelope of the ideal high-pass circuit. This frequency response is the ideal output from the main speakers. Noise High-Pass Filter Filtered Noise Figure 27: Ideal High-Pass Processing Block Diagram. Figure 28: Ideal High-Pass Filtered Noise.

51 Low-Pass Ideal The low-pass ideal circuit is shown in Figure 29, and Figure 30 shows the frequency envelope of the ideal low-pass circuit. This frequency response will be the ideal response from the subwoofer. Noise Low-Pass Filter Filtered Noise Figure 29: Ideal Low Pass Processing Block Diagram. Figure 30: Ideal Low Pass Filtered Noise.

52 Combined Ideal The combined ideal filters are shown in Figure 31. This output will be the ideal response when both the subwoofer and the main speakers play white noise at the same time. Figure 31: Combined Ideal Filters Simulated The simulated results are shown here for a crossover frequency of 120 Hz. They are to be used as a reference as to how the uncorrected simulated speakers behave in a room with a standard crossover.

53 Simulated High-Pass The ideal noise passes through the high-pass filter and then to the simulated speaker. Figure 32 shows the block diagram of the sequence. Figure 33 shows the frequency envelope of the sequence averaged, over 32 points. Noise High-Pass Filter Main Speaker Channel Filtered Noise Figure 32: Simulated High Pass Block Diagram. Figure 33: Simulated High Pass Room and Speaker Response.

54 Simulated Low-Pass The ideal noise passes through the low-pass filter and then to the simulated subwoofer. Figure 34 shows the block diagram of the sequence. Figure 35 shows the frequency envelope of the sequence, averaged over 4 points. Noise Low-Pass Filter Subwoofer Channel Filtered Noise Figure 34: Simulated Low Pass Block Diagram. Figure 35: Simulated Low Pass Room and Speaker Response.

55 Simulated Combined The combined response shows how the speaker and subwoofer should operate when filtered with their respective crossover and combined. Figure 36 shows the simulated combined system. Figure 36: Simulated Combined Room and Speaker Response Crossover Selection During the setup of the system, the algorithm adapts to six discrete crossover points between the frequencies of Hz in steps of 10 Hz. The last filter coefficients were taken from each of the adapting processes and were analyzed to provide the calculated optimum crossover point. It was the amount of gain or reduction required by the filter to provide spectral flatness that was used as a metric for calculating the optimum crossover.

56 49 The crossover frequency that has the smallest gain or reduction after calibration will be used as the optimum crossover frequency. The results are shown in Figure 37. As shown, the crossover frequency of 80 Hz is selected to be the optimum crossover frequency in this case. The 60 Hz and 70 Hz crossover points are there to show that lower crossover frequencies did not help the spectral flatness. Figure 37: Gain/Reduction of equalizing filter Simulated Adaptation The results from the crossover selection and adaptation are shown in the following sections. It is shown that the low frequency adjustment of the filters suffers because of the size of the adaptation filters, which do not provide enough frequency resolution to

57 50 adjust for individual low frequency skews. The frequency resolution of the adaptive filter is about 17 Hz. Before the high pass filter was placed before the ideal response (Figure 14), the corrected response when simulated was flat. However, the actual response placed an extremely large boost in the 20 Hz frequency range that carried over to the other nearby frequencies. The error plots show the error of the identification. It is not possible to perfectly select a filter to inverse the room and speaker response which accounts for the large error. Figures show the results of the simulation and response of the system using the last set of adaptive filter coefficients. For each crossover frequency there is a plot showing the simulated system before correction, the correction filter, after correction, the expected error and the real results. Statistics from the real results were used to come up with a standard deviation and peak-to-peak graph. The results of the standard deviation show that the 80 Hz selected crossover does not provide the minimum standard deviation. The 80 Hz crossover doesn t provide the smallest peak-to-peak but again performs much better than the system without an equalizer or crossover.

58 Figure 38: Simulated real response with 80 Hz crossover. 51

59 Figure 39: Last corrective filter 80 Hz. 52

60 Figure 40: Simulated corrected response with 80 Hz crossover. 53

61 Figure 41: Error plot 80 Hz crossover. 54

62 Figure 42: Actual Response with last Adaptation Coefficients (80 Hz Crossover). 55

63 Figure 43: Simulated real response with 90 Hz crossover. 56

64 Figure 44: Last corrective filter 90 Hz. 57

65 Figure 45: Simulated corrected response with 90 Hz crossover. 58

66 Figure 46: Error plot 90 Hz crossover. 59

67 Figure 47: Actual Response with last Adaptation Coefficients (90 Hz Crossover). 60

68 Figure 48: Simulated real response with 100 Hz crossover. 61

69 Figure 49: Last corrective filter 100 Hz. 62

70 Figure 50: Simulated corrected response with 100 Hz crossover. 63

71 Figure 51: Error plot 100 Hz crossover. 64

72 Figure 52: Actual Response with last Adaptation Coefficients (100 Hz Crossover). 65

73 Figure 53: Simulated real response with 110 Hz crossover 66

74 Figure 54: Last corrective filter 110 Hz. 67

75 Figure 55: Simulated corrected response with 110 Hz crossover. 68

76 Figure 56: Error plot 110 Hz crossover. 69

77 Figure 57: Actual Response with last Adaptation Coefficients (110 Hz Crossover). 70

78 Figure 58: Simulated real response with 120 Hz crossover. 71

79 Figure 59: Last corrective filter 120 Hz. 72

80 Figure 60: Simulated corrected response with 120 Hz crossover. 73

81 Figure 61: Error plot 120 Hz crossover. 74

82 Figure 62: Actual Response with last Adaptation Coefficients (120 Hz Crossover). 75

83 Figure 63: Simulated real response with 130 Hz crossover. 76

84 Figure 64: Last corrective filter 130 Hz. 77

85 Figure 65: Simulated corrected response with 130 Hz crossover. 78

86 Figure 66: Error plot 130 Hz crossover. 79