EE342.01: MATLAB M-FILE FOR COMPARING DTFT AND DFT SPECTRA

%
% Filename: example14.m
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% Description: m-file for comparison of DTFT and DFT
%

clear;                      % clear matlab memory

N = 4;                      % number of data points in x[n], Xk

W = 0:0.01:2*pi;            % define DT frequencies
X = 2+exp(-j*W)+2*exp(-j*2*W)+exp(-j*3*W); % define DTFT

k = 0:N-1;
Wk = 2*pi*k/N;              % define sampled DT frequencies
Xk = [6 0 2 0];             % define DFT values

subplot(2,1,1);             % plot magnitude spectra
plot(W,abs(X)); hold on;
stem(Wk,abs(Xk),'filled'); hold off;
xlabel('\Omega ');
ylabel('|X|');
title('Magnitude Spectra from DTFT X(\Omega) and DFT X_k');
legend('|X(\Omega)|', '|X_k|');

subplot(2,1,2);             % plot phase spectra
plot(W,angle(X)*180/pi); hold on;
stem(Wk,angle(Xk)*180/pi,'filled'); hold off;
xlabel('\Omega ');
ylabel('Angle(X) ');
title('Phase Spectra from DTFT X(\Omega) and DFT X_k');
legend('Angle(X(\Omega))', 'Angle(X_k)');