How do I plot the impulse response of a sound?

My assignment is to write a Matlab program that generates sounds using parametric resonators. The ultimate goal is to produce an interesting sound built from concatenated and/or summed outputs from these second order resonators. I can start with an 8kHz sample rate and produce decaying tones at frequencies of my choice. I need to plot some pulse responses and frequency responses.

I believe I have the frequency response at 8K Hz using the freqz() function. I'm not sure how to get the impulse response. Here is my code so far:

% Resonance program in matlab

fs=input('please enter a value for fs'); % Audio sampling rate (Hz)

N = 2*fs; % 2 seconds of data, time length

w0 = pi/8; % frequency - 16 cycles to go around unit circle

R = .999;

a1 = -2.*R.*cos(w0);

a2 = R*R;

G = (1-R).*sqrt(1-2*R*cos(2*w0)+R*R);

b0= G;

b = b0; % feed forward

a = [1 a1 a2]; % feedback

[H,w]=freqz(b,a,2^12);

plot(w, abs(H));

xlabel('Radians per Sample');

ylabel('Magnitude');

title('Frequency Response at 8000 Hz');

I = filter(b,a,[1,zeros(1,500)]); %impulse response

stem ([0:500],I);

xlabel('Samples');

ylabel('Amplitude');

title('Impulse Response at 8000 Hz');

pls=[1 zeros(1,N-1)]';

hpls=filter(b,a,pls);

plot (hpls);

soundsc(hpls, fs);

xlabel('radians per sample');

ylabel('Magnitude');

title('Sound for 2 Second');

Thanks in advance!

Answer 1

[Mahesh Taparia]

Hi Ashley,

You can use impz, an inbuilt function in MATLAB to find the impulse response of discrete system. After finding transfer function, instead of using 'imfilter' you can use the below command to find the impulse response:

impz(b,a,16000,8000); 

For more information, you can refer to documentation page of impz here.

[Ashley Rudolph]

Thank you very much!