%Demo done during Session 22 to illustrate
%the effects of truncating a sum of
%two sinewaves -- we analyze the effects
%as a function of the separation in
%frequency and the differential in
%amplitude amongst the two sinewaves
%
clf
set(0,'defaultaxesfontsize',22);
x=cos(2*pi*6.5*(0:31)/32)+cos(2*pi*6*(0:31)/32);
freqomega=linspace(-pi,pi,1024);
z=abs(fftshift(fft(x,1024)));
fmag=20*log10(abs(z));
fmag=fmag-max(fmag);
clg
plot(freqomega,fmag,'LineWidth',4);
axis([-pi pi -30 0]);
title('DTFT of Two Closely-Spaced Sinusoids'),...
xlabel('Omega'), ylabel('Magnitude (dB)'), grid
hold on
Ws1=2*pi*(6/32); Ws2=2*pi*(6.5/32);
plot([Ws1 Ws1],[-30 0],'m--','LineWidth',4)
plot([Ws2 Ws2],[-30 0],'m--','LineWidth',4)
hold off
pause
x=20*cos(2*pi*5*(0:31)/32)+cos(2*pi*12*(0:31)/32);
z=abs(fftshift(fft(x,1024)));
fmag=20*log10(abs(z));
fmag=fmag-max(fmag);
clg
plot(freqomega,fmag,'LineWidth',3);
axis([-pi pi -30 0]);
title('DTFT of Two Sinusoids with Diverse Amplitudes'),...
xlabel('Omega'), ylabel('Magnitude (dB)'), grid
hold on
Ws1=2*pi*(5/32); Ws2=2*pi*(12/32);
plot([Ws1 Ws1],[-30 0],'m--','LineWidth',4)
plot([Ws2 Ws2],[-30 0],'m--','LineWidth',4)
hold off