Question

Use MATLAB to compute the convolution as a sum ofechoes of the input signal x[n] = cos () with the impulse response h[n]1.5un un - 6]) of an LTI system S. Is the output periodic? Why or why not? Please explain.

Answer 1

n=-7:30;
x=cos(2*pi*n/5);
h=1.5*(ones(1,7));
m=length(x);
n=length(h);
X=[x,zeros(1,n)];
H=[h,zeros(1,m)];
for i=1:n+m-1
Y(i)=0;
for j=1:m
if(i-j+1>0)
Y(i)=Y(i)+X(j)*H(i-j+1);
else
end
end
end
stem(Y);
ylabel('Y[n]');
xlabel('----->n');
title('Convolution of Two Signals without conv function');

Convolution of Two Signals without conv function 1.5 0.5 0.5 -1 -2 -2.5 0 5 10 15 20 253035 40 45

Yes output is periodic,from convolution property output is periodic if atleast one of the input are periodic, here only x[n] is periodic but not h[n], So y[n] is periodic

Convolution of Two Signals without conv function 1.5 0.5 0.5 -1 -2 -2.5 0 5 10 15 20 253035 40 45