EE342: MATLAB M-FILE DEMONSTRATING RELATIONSHIP BETWEEN CFT AND ITS DFT APPROXIMATION THROUGH SAMPLING

%
% Filename: example13.m
%
% Description: M-file demonstrating the use of the DFT for 
%              approximating continous-time frequency content.
%

figure(1);
clear; clf;                      % clear memory and figure

t = 0:0.0000005:0.00015;         % CT and CT signal
ft = (1 + cos(2*pi*20000*t)).*cos(2*pi*100000*t);
subplot(2,2,1); plot(t,ft);
xlabel('t (sec)'); ylabel('f(t)');
title('CT AM Signal');

f = [-100000 100000 -80000 80000 -120000 120000];
F = [pi pi pi/2 pi/2 pi/2 pi/2];% CTFT of CT signal
subplot(2,2,2); stem(f,F,'^');
xlabel('f (Hz)'); ylabel('F(f)');
title('CTFT of CT AM Signal');

T = 0.0000025;                  % compute and plot DT signal
k = 0;
for m = 0:5:length(ft)-5,
  fk(k+1) = ft(m+1);
  kvec(k+1) = k;
  k = k + 1;
end;
subplot(2,2,3); stem(kvec,fk,'filled');
xlabel('k'); ylabel('f[k]');
title('f[k] from Sampling CT AM Signal');

fkpad = [fk zeros(1,20)];       % compute & plot padded DT signal
kvecpad = [kvec 60:79];
subplot(2,2,4); stem(kvecpad,fkpad,'filled');
xlabel('k'); ylabel('f[k]');
title('Padded f[k]');

figure(2); clf;                 % open & clear figure 2

Fr = dft(fkpad);                % compute and plot DFT mag spectrum
r = kvecpad;
stem(r/(80*T), abs(Fr),'filled');
xlabel('f = r/NoT (Hz)'); ylabel('|Fr|');
title('Magnitude Spectrum from DFT of Sampled Signal');