AUDL Signals & Systems for Speech & Hearing Week I You may find this course demanding! How to get through it: Consult the Web site: www.phon.ucl.ac.uk/courses/spsci/sigsys Essential to do the reading and suggested exercises Laboratory sessions go a long way to clarify the material presented Bring questions to the tutorial sessions Keep up with the work If you have problems, ask for help! If you can do the course work and exercises, you will do well on the exam if you cannot, you will not! What is sound? Plotting a pressure wave over time: Sound is oscillation of air pressure (pressure wave). high pressure: air molecules bunched up low pressure: air molecules spread out Air molecules do NOT travel through space to carry sound!! Sound is a SIGNAL
A very simple signal: Sinusoids can only differ in three ways displacement (mm) pressure (Pa) - - - sinusoid or pure tone.2.4.6.8. In other words, once you know a wave is sinusoidal, there are only three things to know about it: frequency amplitude phase (generally less important because phase changes are typically not perceived) I: Periodicity (frequency) Specifying periodicity Pressure displacement (mpa) (mm) - - - 2.27 ms.2.4.6.8. The period (p) is the time to complete one cycle of the wave Alternatively, the number of cycles that are completed in one second, is the frequency (f) f=/p and p=/f here =/.227 sec = 44 cycles per second (cps) But a special unit name is used
Keep your units consistent! hertz (Hz): a measure of frequency period of. sec = ms (millisecond) so: period in seconds: f (Hz)=/p (s) period in ms: f (Hz)=/p (ms) period in ms: f (khz) =/p (ms) A period of ms =?? Hz A frequency of Hz =?? ms Increases in frequency (decreases in period) lead to increases in subjective pitch amplitude 5 Hz - 2 3 4 5 Hz - 2 3 4 5 2 Hz - 2 3 4 5 time (ms) displacement (mm) Pressure (mpa) - - - mpa II: Amplitude.2.4.6.8.
Increases in amplitude lead to increases in perceived loudness amplitude Most intense - 2 3 4 5 attenuated by a factor of 4-2 3 4 5 attenuated by another factor of 4-2 3 4 5 time (ms) Measures of amplitude It is crucial to distinguish instantaneous measures (as in a waveform) from some kind of average Instantaneous measures always linear (e.g., pressure in Pa, voltage in V, displacement in metres) But also want a single number to be a good summary of the size of a wave Average measures can be linear or logarithmic (db) displacement voltage (V) (mm) Simple measures of amplitude peak amplitude = V - - - peak-to-peak amplitude = 2 V.2.4.6.8. Drawback to peak measures Don t accurately reflect the energy in a waveform displacement voltage (V) (mm) - - -.2.4.6.8.
root-mean-square (rms) Square all the values of the wave Take the average area under the curve Take the square root A measure of the energy, applicable to all waveforms Similar to calculating a standard deviation Still a linear measure (Pa, mm, V) - - -.2.4.6.8. rms=.77 Scaling amplitude: The decibel Scale Idea I: Define a point of reference and rescale data in terms of that reference Idea II: Use a kind of warped scale that relates to perception London (km ) Imagine a bank robbery between London and Edinburgh: 48 km caught 35.7 km Robbers have accident 358 km Bank robbery 362.8 km Robbers kidnap witness London (- 358 km) Declare a reference point - 3 km caught - 7.3 km robbers have accident km Bank robbery + 4.8 km Robbers kidnap witness 349.5 km seen again Edinburgh (km 753) -8.5 km seen again Edinburgh (+ 395) 352.3 km Robbers change car 357 km Robbers release witness 36 km seen st time 7 km Police block road - 5.7 km Robbers change car - km Robbers release witness + 3.5 km seen st time + 352 km Police blocks road
Warp the scale data Rescale data London (- 358 km) - 3 km caught - 7.3 km robbers have accident km Bank robbery + 4.8 km Robbers kidnap witness London (- 358 km) - 3 km caught - 7.3 km robbers have accident + 4.8 km Robbers kidnap km witness Bank robbery -8.5 km seen again - 5.7 km Robbers change car - km Robbers release witness + 3.5 km seen st time + 352 km Police blocks road Edinburgh (+ 395) -8.5 km seen again - 5.7 km Robbers change car - km Robbers release witness + 3.5 km seen st time Edinburgh (+ 395) + 352 km Police blocks road Acoustic sound levels Acoustic sound levels µpa no sound atmospheric pressure 2 µpa threshold of hearing 2 µpa whisper µpa normal speech µpa pop group µpa jet engine µpa no sound atmospheric pressure 2 µpa threshold of hearing db 2 µpa whisper µpa normal speech µpa pop group µpa jet engine 2 µp threshold of pain Reference point: Sound pressure level scale (SPL) Warped 2 µp threshold of pain
µpa no sound atmospheric pressure 2 µpa threshold of hearing db 4 db 2 µpa whisper µpa normal speech 54 db 94 db Idea II: Relate to perception µpa pop group µpa jet engine 2 µpa pain! 34 db 4 db a)find reference point and rescale: refer to threshold of hearing ( db SPL) b) Warp the scale to reflect perception: e.g. 2 µpa more detailed e.g. 2 µpa less detailed Logarithmic scaling represents human hearing c) Handle big numbers: 2-2 µpa 4 db How to rescale data? Logarithms! Logarithms are a way of saying Ten to the power of what is this number? For example: log () Ten to the power of what is? Ten to the power of two is 2 = Therefore log () is 2. Logarithms convert numbers into powers of Logarithms are simple! log ()=?? rewrite as a power of? = 3 = log ( 3 )=?? log ()=3
Examples of logarithms log() =?? log() = because = log(.) =?? log(.) = because =. log() =?? log() = because = So log of a number that is greater than is positive log of a number that is less than is negative not only integers log(5) =.699 makes sense! log(-) =??! Sound Pressure Level Pressure( Pa) Intensity( dbspl) = 2log 2µ Pa 2µPa is standard reference pressure approximately equal to human threshold log (ratio) turns ratio into power of. Measuring amplitudes with db Not a linear unit like pascals A logarithmic measure with an arbitrary reference point db does not mean no sound; it means the same as the reference Any positive number of db means greater than the reference (e.g., db) Any negative number of db means less than the reference (e.g., - db) Many different kinds of db (SPL, HL, ) which differ essentially in the meaning of db. db SPL Examples Threshold of Hearing (2 µpa) 2 log (2 µpa/2 µpa) = 2 log () = 2 = db SPL Threshold of Pain (2 Pa) 2 log (2 Pa/2 µpa) = 2 log () = 2 7 = 4 db SPL An inaudible sound (2 µpa) 2 log (2 µpa /2 µpa) = 2 log (.) = 2 - = -2 db SPL
Human hearing for sinusoids Getting a feel for decibels (db SPL) db SPL ULL ------------------- threshold dynamic range threshold (db SPL) Thresholds for different mammals 8 7 6 5 4 3 2 - frequency (Hz) hum an poodle m ouse Why use a logarithmic unit (db)? Waveforms can be specified in linear rms units and often are, But our perception of changes in sound amplitude is more closely related to a logarithmic scale (based on ratios/proportions) Compare distinguishing a khz sinusoid of 5 µpa vs. µpa (obvious change) And Pa to ( Pa + 5 µpa) =.5 Pa (indistinguishable)
Just-noticeable difference in intensity is about db Standard -db less intense 3-dB less intense 6-dB less intense -db less intense Amplitude and Intensity Strictly, db SPL scale is a measure of relative intensity (intensity = amount of energy delivered per unit area per unit time) However intensity turns out to be simply related to amplitude, and so we use amplitude in the db SPL formula (also explains why the multiplier is 2 instead of, for deci- ). db can be used for any amplitude measure as long as a reference Pressure( is defined. Pa) Sound Pressure Level ( dbspl) = 2log 2µ Pa db scales are used widely db can be used for any amplitude measure as long as a reference is defined. db re mv = 2 * log (x mv/ mv) where x is any number V = 2 * log ( mv/ mv) = 6 db re mv V = 2 * log ( V/ V) = db re V Can use db for displacement (meters), current (amps), etc. Can use db for sound pressure but a different reference in place of 2 µpa What this is all for What s the most commonly used piece of electronic equipment in the audiological clinic? The Audiometer
The minimalist audiometer needs And what is its purpose? An oscillator to generate an electrical sinusoidal wave at the desired frequencies A calibrated volume control to adjust the intensity of the sound A headphone to convert the electrical wave to an acoustic one, so it can be presented to the listener The minimal audiometer What comes out of the oscillator? change frequency change amplitude (2 ways) Electrical wave (to be graphed as a waveform) A graph of the instantaneous value of the voltage (or current), across time Crucial for every waveform x-axis is always time (s, ms, µs) y-axis always a linear instantaneous amplitude measure (V, mv, µv) But oscillators usually give a very special waveform, a sinusoid, also known as a pure tone (at least in reference to sounds)
displacement (mm) voltage (V) An electrical sinusoidal waveform from an oscillator - - -.2.4.6.8. 2 ms 4 ms 6 ms 8 ms ms Transducing an electrical wave to an acoustic one We cannot hear an electrical wave directly, so need to convert it by feeding to the headphones which transduce the variations in the electrical wave to a mechanical wave the changes in voltage cause the headphone diaphragm to vibrate, which makes the sound time Just like a miniature loudspeaker Movement of the headphone diaphragm http://electronics.howstuffworks.com/speaker5.htm displacement (cm) displacement (mm) - - -.2.4.6.8.