%% dft1demo2
%% show a signal and dft pair
%% the dft is shifted to put low frequencies in the center 

% define signal, sample rate, sample domain
N = 512;
t = (0:1:(N-1))/N;
I = sqrt(-1);
%sig = 2*cos(5*2*pi*t)+0.5*sin(24*2*pi*t);
%sig = 2*cos(3*2*pi*t)+0.5*sin(5.4*2*pi*t);
% k = round(0.95*N); sig = [ones(1,k),zeros(1,N-k)]*(N/k);
% k = 2; sig = [ones(1,k),zeros(1,N-k)]*(N/k);
 k = round(0.95*N); sig = [ones(1,k),zeros(1,N-k)]*(N/k); sig = sig - mean(sig);
%sig = rand(1,N);
%sig = 2*rand(1,N)-1;
%sig = 2*cos(5*2*pi*t)+ I*0.5*sin(24*2*pi*t);
%sig = cos(5*2*pi*t);
%sig = sin(5*2*pi*t);
%sig = t.*(1-t);
%sig  = t;
%sig  = [0:1:(N/2-1),(N/2-1):-1:0]-N/4; 


SD = 0:(N-1);

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

FD = fftshift(SD);
N1 = FD(1);
FD(1:(N-N1))=  (N1-N):(-1);


% display results 
figure(1)
subplot(2,1,1)
plot(SD,real(sig),'r',SD,imag(sig),'g')
title('sampled signal');
axis tight
subplot(2,1,2)
plot(FD, real(sfsig),'r',FD,imag(sfsig),'g')
title('shifted DFT of signal')
axis tight
figure(2)
subplot(2,1,1)
plot(FD, abs(sfsig),'r-' )
title('magnitude of shifted DFT')
subplot(2,1,2)
plot(FD, angle(sfsig),'g-' )
title('phase of shifted DFT')
figure(3)
plot(fsig,'.')