% Demo of DFTs of cosines
% Upgraded to included DTFT analysis
% Last revised 10/7/97 - rms

%Create a cosine with period 16

clear

N0 = 16;
n = 1:64;
np = n-1;
xn = cos(2*pi*np/N0);

subplot(1,1,1),stem(0:63,xn(1:64))
title('Cosine with period of 16 samples')
pause

% Show the 64-point DFT
Xk = fft(xn(1:64),64);
stem(0:63,abs(Xk))
title('64-point DFT')
pause

% Show the 60-point DFT
Xk = fft(xn(1:60),60);
stem(0:59,abs(Xk))
title('60-point DFT')
pause


% Compare the two time functions
np2 = 0:79;
xnp1 = [xn xn(1:16)];
subplot(2,1,1), stem(np2,xnp1)
hold on
subplot(2,1,1), stem(64:79,xn(1:16),'r')
hold off

xlabel('n')
title('16-point cosine repeated with period 64')

xnp2 = [xn(1:59) xn(1:21)];
subplot(2,1,2), stem(np2,xnp2)
hold on
subplot(2,1,2), stem(59:79,xn(1:21),'r')
hold off
xlabel('n')
title('16-point cosine repeated with period 60')

pause

% Show DTFT and DFT of 64-point cosine
ovsamp = 8;		% How many times we oversample for display
w = -pi:pi/(64*ovsamp/2):pi;	 
w2 = w(1:(ovsamp*64));
% temp = .5*sincN(64,w2);
temp = .5*64*diric(w2,64);
X = cirshftt(temp,4*ovsamp,64*ovsamp) + cirshftt(temp,-4*ovsamp,64*ovsamp);
subplot(1,1,1),plot(w/pi,[X X(1)])
hold on
title('DTFT')
xlabel('w/pi')
pause

index = 1+ ovsamp*(0:63);
stem([w(index)/pi 1],[X(index) X(1)],'r')
title('DTFT and 64-point DFT')
pause
hold off


% Repeat, but for N = 60

ovsamp = 8;		% How many times we oversample for display
w = -pi:pi/(64*ovsamp/2):pi;	 
w2 = w(1:(ovsamp*64));
% temp = .5*sincN(64,w2);
temp = .5*64*diric(w2,64);
X = cirshftt(temp,4*ovsamp,64*ovsamp) + cirshftt(temp,-4*ovsamp,64*ovsamp);
subplot(1,1,1),plot(w/pi,[X X(1)])
hold on
title('DTFT')
xlabel('w/pi')
pause

Y = resample(X,15,16);	% Resampling to new DFT points
index = 1+ ovsamp*(0:59);

w3 = -pi:(16/15)*pi/(64*ovsamp/2):pi;	 
stem([w3(index)/pi 1],[Y(index) Y(1)],'r')
title('DTFT and 60-point DFT')
pause