Question

Hi, can someone help me obtain the Figure 1 graph using Matlab? I need to see the code how you do the DTFT in Matlab. Thanks!

The impulse response of a discrete-time LTI (linear time-invariant) system is, h[n] = Sinna Refer to Table 5.2 in the textbook for the basic discrete-time Fourier transform pairs The frequency response of the LTl system is, H (ejo, Here, H(e") is periodic with period 2 Step 2 of 31 Sketch the frequency response of the system He* ) Figure 1

Answer 1

MATLAB code is given below in bold letters followed by the frequency response plot.

clc;
clear all;
close all;

nmax = 1000;
n = -nmax:nmax;
W = 1;% lets say W=1
h = sin(W*n)./(pi*n);
h(nmax+1) = W/pi;
w = -2*pi:0.01:2*pi;
for k = 1:length(w)
H(k) = sum(h.*exp(-1j*w(k)*n));
end

figure;plot(w,H);grid;xlabel('w');ylabel('Amplitude');
title('Spectrum of h[n]:H(exp(jw))');

*** As the number of terms increase, the ripple will decrease.