EE599-020 Audio Signals and Systems

1. EE599-020Audio Signals and Systems Psychoacoustics (Masking) Kevin D. DonohueElectrical and Computer EngineeringUniversity of Kentucky

2. 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.

3. 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.

4. 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.

5. Example Broadband Signal Spectra Sound Sequence: Starting with the largest band

6. 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);

7. Broadband Noise Script 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') • % 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 • 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

8. 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?

9. 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.

10. Example 2 Tones Spectrogram 2000 Hz and 2100 Hz pair

11. Example 2 Tones Spectrogram 2000 Hz and 3090 Hz pair

12. 2-Tone Function • 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

13. 2-Tone Script • % 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 • (Continued on next slide …)

14. 2-Tone Script - Continued • % 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

15. 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?

16. 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).

17. Gammatone Filters The Gammatone filter impulse response: where  = 4, fc is the center frequency, and b is set to match the bandwidth of the critical band.