%% dftdemo2
%% show a signal and dft pair
%% the dft is shifted to put low frequencies in the center 

% define signal, sample rate, sample domain
N = 128;
t = (0:1:(N-1))/N;
% sig = 2*cos(5*2*pi*t)+0.5*sin(24*2*pi*t);
k = 20; sig = [ones(1,k),zeros(1,N-k)]*(N/k);
SD = 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 
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)
plot(FD, abs(sfsig),'r-')