Question

Zero-state response of a system can be found by using convolution of the input signal and unit impulse response: Use conv command from MATLAB to compute the zero-state response of the system defined in part B to the input x[n] in part C. 1. 2. 3. Is the result same as what you found in part (C)? Is this system asymptotically stable? Why?

I need help with this MATLAB exercise.

The given system is y[n] - (3/10)y[n-1] - (1/10)y[n-2] = 2x[n]

The input x[n] is 2cos(2*pi*n/6)(u[n] - u[n-10])

Don't have to answer part 2 of the question.

Answer 1

Hello,
       Please find the answer attached below. If the answer has helped you please give a thumbs up rating. Thank you and have a nice day!

********** Matlab code for plotting the convolution *********

b = 2;              %filter coefficients
a = [1 -0.3 -0.1];
[h,n] = impz(b,a); % impulse response
x = 2*cos(2*pi*n/6).*double(n<10);
y = conv(h,x);      % convolution
stem(y);
grid;
xlabel('N');
ylabel('Y');
title('Output by convolution');

************** End of file ************

Output:

Output by convolution

The systemk is asymptotically stable since the impulse response, as well as the convoluted response both are damped responses.

***********************************************************

PS: Please do not forget the thumbs up!!