% DFT program homework on April 4, 2007
% version 2
% message is a sinusoid
    N=128;
    f0=0.1;
    f1=0.4;
    t=[0: 1: 127];
    g0=sin(2*pi*f0*t);
    g1=cos(2*pi*f1*t);
    
     zz0=fft(g0);
     z0=fftshift(zz0);   
     % fftshift makes the center to be 0Hz instead of half of the sampling
     % frequency
     zz1=fft(g1);
     z1=fftshift(zz1);
     Ts=t(2)-t(1);  % the sampling period
     Fs=1/Ts;       % the sampling frequency in Hz
     F = Fs*(-N/2:(N/2)-1)/N;   % frequency axis
     plot(F, abs(z0+z1));
     y0=ifft(z0);
     y1=ifft(z1);
  
% DFT program 
% put the DFT result in an array u0 and u1
% plot(abs(u0+u1)) and compare it with the result by plot(abs(z0+z1))
  
% IDFT prgram
% put the IDFT result in arrays w0 and w1  
% compare these with g0 and g1