EE599-020
Audio Signals and Systems
Psychoacoustics (Masking)
Kevin D. Donohue
Electrical and Computer Engineering
University of Kentucky
Critical Bands
The band-pass properties observed for the basilar
membrane results in a frequency dependence for
our ability to perceive loudness and detect tones in
a complex excitation signal.
The bandwidths of critical bands follow an
approximate 1/3 to 1/6 octave relationship with
the center frequency.
1
Bc 
f c for f c  500 Hz
3 2
Bc 
1
6 2
f c for f c  500 Hz
Loudness and Critical Band
Tones separated by distances greater than the
critical band are perceived louder than the
same tones within a critical band.
Broadband noises spanning several critical
bands are perceived louder than broadband
noise of the same power within one critical
band.
Example Broadband
A function was created to generate white Gaussian
noise with unit power in a designated frequency
band and specific sampling rate. A series of band
pass filters and scalings were applied to keep the
power in the noise constant with frequency bands
reducing on a center frequency around 2120 Hz.
Example Broadband Signal
Spectra
Number of
critical bands
in each sound
-3
x 10
Sound
Sequence:
Starting
with the
largest band
2.5
PDS
2
1.5
Approximate Critical Band
1
0.5
0
500
1000
1500
2000
2500
Hertz
3000
3500
4000
14.7
8.1
2.2
1.0
0.5
0.2
Broadband Noise Function
function [sig, t] = broadb(f1,f2,int,fs)
% This function creates white Gaussian noise in the frequency band
% starting with F1 and ending with F2 in Hertz, with sampling frequency
% FS for a duration of INT seconds.
%
%
[sig, t] = broadb(f1,f2,int,fs)
%
% The output is a row vector SIG containing the sampled points
% of the noise. T is an optional output and is the time axis
% assoicated with SIG.
%
% Written by Kevin D. Donohue (donohue@engr.uky.edu) June 2003
t = [0:fix(fs*int)-1]/fs; % Create time axis
ord = round(.15*fs); % compute filter order to cover 150 ms
ns = randn(1,length(t)+2*ord-2); % Generate WGN - full band
% Create FIR filter to obtain the bandlimited white noise
amp = [0 0 1 1 0 0]; % Spectral amplitudes of filter
fre = [0 f1-10 f1+10 f2-5 f2+5 fs/2]/(fs/2); % corresponding to these normalized frequecies
b = fir2(ord,fre,amp); % Generate filter coefficients
sig = filtfilt(b,1,ns); % Filter signal and reversed version to eliminate boundary and delay effects
% Normalize power to ensure constant level
sig = sig/std(sig);
Broadband Noise Script
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% This script generates 6 example noise signals, with
% sucessively smaller bandwidths. The last 2 are within
% the critical band.
% The average spectrum (PSD) for each is plotted and the
% signals are concatenated together as save as a wave file.
% You need the functions BARKCOUNT and BROADB
% to run this script.
%
% Written by Kevin D. Donohue (donohue@engr.uky.edu)
% February 2004
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fs = 11025; % Sampling Frequency
dur = 2; % Sound duration in seconds
% Vectors describing the sucessive bandlimit on the sounds
f1 = [270, 1000, 1800, 2000, 2050, 2100]; % lower limit
% corresponding upper bandlimit
f2 = [4000, 3500, 2500, 2320, 2220, 2150];
% colors for the PSD plots
col = ['g', 'r', 'b', 'k', 'c', 'b'];
% Loop to create each sound and concatenate into one
% vector
fsig = []; % Initialize vector to concatenate sounds
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for k=1:length(f1);
% Generate noise
no(k,:) = broadb(f1(k), f2(k), dur, fs);
fsig = [fsig, no(k,:)]; % Concatenate
% Count the bark (Critical Bands)
cb(k) = barkcount(f1(k),f2(k));
% Compute PSD of noise
[p, fax] = psd(no(k,:),1024, fs, hamming(512));
figure(1);
% Plot PSD
lh = plot(fax,abs(p)/(length(no(k,:))),col(k))
set(lh,'LineWidth',2) % Make line thicker
hold on
end
hold off
% Label figure
xlabel('Hertz')
ylabel('PDS')
% Write sound to wavefile
wavwrite(fsig/(max(abs(fsig)+eps)), fs, 'wgncritband.wav')
Example Discussion
Why did the first 3 signals sound louder than
the last 3 signals, even though they were all at
the same power level?
If a tone was played at 2120 Hz with the
sounds of this example, which broadband
sounds would be more likely to mask it?
Example 2 Tones
Generate 2 tones in the same critical band (at
2000 and one at 2100 Hz). Play a sequence of
the pure reference tone followed by a
combination of the test and reference tones
where the test tone is reduce by 5 dB each
time. Count the number of times you heard
the test tone. Repeat with test tone at 3090
Hz.
Example 2 Tones Spectrogram
Masking Illustration: 2000 masking 2100
3500
dB
45
3000
Hertz
40
35
2500
30
2000
25
1500
0
5
10
15
Seconds
20
25
20
2000 Hz and
2100 Hz pair
Example 2 Tones Spectrogram
3500
45
3000
Hertz
40
35
2500
30
2000
25
1500
0
5
10
15
Seconds
20
25
20
2000 Hz and
3090 Hz pair
2-Tone Function
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function [v, t] = tonec(f,int,fs)
% This function will create a series of samples at sampling rate
% FS for a duration of INT seconds at frequencies in the frist column
% of vector F in Hertz. The second column of F will be the weight for
% each tone. If a second column is not given then an equal scaling of
% of will be given to each tone.
%
%
[v, t] = tonec(f,int,fs)
%
% The output is a row vector V containing the sampled points
% T is an optional output and is the time axis assoicated with V.
%
% Written by Kevin D. Donohue (donohue@engr.uky.edu) 6/2003
[r, c] = size(f); % Check dimension of f
% Ensure frequency values are in different rows
if c > 2 % if not transpose
f = f';
[r, c] = size(f);
end
% Check to see if coefficients for frequenies are provided
if c == 1 % If not set them = to one
f(:,2) = ones(length(f),1);
end
t = [0:fix(fs*int)-1]/fs; % Create time axis
v = zeros(size(t)); % initialize vector to accumulate multiple tones
for k=1:r
v = v + f(k,2)*sin(2*pi*t*f(k,1)); % Create sampled tone signal
end
2-Tone Script
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% This script generates tone pair signals, with successively
% smaller amplitudes on a test to illustrate masking
% The signal pair are generate individually and concatenate
% together with silence and reference tones stuffed in between
% and saved as a wave file.
% This script needs the TONEC function to run.
%
% Written by Kevin D. Donohue (donohue@engr.uky.edu) June 2003
fs = 11025; % Sampling Frequency
dur = 1;
% Tone duration
reffre = 2000; % Reference tone
tfre = 2100; % Test tone with decreasing volume
% Vector with sequence of relative volume levels
tamp = 10.^([0 -5 -10 -15 -20 -25 -30 -35 -40 -45]/20);
reftone = tonec([reffre 1], dur, fs); % Generate Reference tone signal
outsig = []; % Initalize output matrix for concatenation
scil = zeros(1,round(fs*dur/2)); % Create silence interval
% Loop to build complex tone, concatenation with reference and rest of
% sequence
for k=1:length(tamp)
ttone = tonec([reffre 1; tfre tamp(k)], dur, fs);
outsig = [outsig scil reftone scil std(reftone)*ttone/std(ttone)];
end
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(Continued on next slide …)
2-Tone Script - Continued
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% Write test signal
wavwrite(outsig/(max(abs(outsig)+eps)), fs, 'testttsig2.wav')
% Create and plot spectrogram
[B,F,T] = SPECGRAM(outsig,4*512,fs,hamming(4*256),4*128);
imagesc(T,F,20*log10(abs(B)+10))
axis('xy')
axis([T(1) T(end) 1500 3500])
xlabel('Seconds')
ylabel('Hertz')
title(['Masking Illustration: ' num2str(reffre) ' masking ' num2str(tfre)])
colorbar
2-Tone Discussion
How many times did you hear the test tone for the 2000 and
2100 Hz pair? How many times did you hear the test tone for
the 2000 and 3090 Hz pair?
Estimate the masking threshold for tones separated by 100
Hz near 2000 Hz.
Estimate the masking threshold for tones separated by 1090
Hz near 2000 Hz.
Why is there a difference?
Is it possible to eliminate the beat frequencies for closely
place tones?
Gammatone Filters
The Gammatone filter:
Is physically realizable (causal)
Provides a good fit to the impulse response
of the auditory nerve fibers (Carney and Yin
1988, J. Neurophys. 60, 1653-1677).
Gammatone Filters
The Gammatone filter impulse response:
b t ( 1) exp( 2bt ) cos( 2f ct   ) for t  0
h(t )  
for t  0
 0
where  = 4, fc is the center frequency, and b is
set to match the bandwidth of the critical band.