%% dftdemo3
%% show how DFT captures frequency

% define signal, sample rate, sample domain
steps = 32;
N = 64;
t = (0:1:(N-1))/N;
I = sqrt(-1);
sig = 2*cos(2*2*pi*t)+0.5*sin(7*2*pi*t);
%sig = 2*cos(5*2*pi*t)+0.5*sin(10*2*pi*t);
%k = 45; sig = [ones(1,k),zeros(1,N-k)]*(N/k);
%sig = rand(1,N);
%sig = 2*rand(1,N)-1;
%sig = 2*cos(5*2*pi*t)+ I*3*sin(7.1*2*pi*t);
SD = 0:(N-1);

% get dft and frequency domain
fsig = fft(sig); 
FD = 0:(N-1);

% display results 
figure(1)
subplot(2,2,1)
plot(SD,real(sig),'r-',SD,imag(sig),'g-')
title('sampled signal');
axis tight


for k = 0:steps 
subplot(2,2,2)
plot(FD,real(fsig),'r-',FD,imag(fsig),'g-', [k],real(fsig(k+1)),'k*',[k],imag(fsig(k+1)),'k*')
axis tight
title('DFT'); 
E = exp(2*pi*I*k*t);   
subplot(2,2,3)
plot(SD, real(E),'r-',FD,imag(E),'g-')
axis([0 (N-1) -1.1 1.1]);
title('pure wave form')
axis tight
subplot(2,2,4)
plot(SD, real(sig.*conj(E)),'r-',SD, imag(sig.*conj(E)),'g-', SD,zeros(size(SD)),'k-' );
title('product of signal and waveform');
axis tight
pause;
end