%% dftdemo
%% show a noisy signal and shifted dft magnitude
%% smooth dft and then smooth signal

% define signal, sample rate, sample domain
N = 256;
t = (0:1:(N-1))/N;
truesig = cos(5*2*pi*t)+0.5*cos(24*2*pi*t);
noise = rand(size(truesig)) - 0.5*ones(size(truesig)); 
sig  = truesig+noise;

SD = 0:(N-1);

% get dft and frequency domain
csig = dct(sig); 
FD = (0:(N-1))/2;

csig =dct(sig);


% display signal and transform 
figure(1)
subplot(2,1,1)
plot(SD,real(sig),'r')
title('sampled signal');
axis tight
subplot(2,1,2)
plot(FD, csig,'r-' )
title('frequency stength')
axis tight

% smooth transform and signal
thresh =0.1;
m = max(abs(csig)); 
ZI = find(abs(csig) < thresh*m);
smcsig = csig;
smcsig(ZI) = 0;
smsig = idct(smcsig);
disp('press a key');
pause

% display smoothed functions 
figure(2)
subplot(2,1,1)
plot(FD, smcsig,'r-' )
title('thresholded DCT')
axis tight
subplot(2,1,2)
plot(SD, smsig,'r-' )
title('smoothed signal')
axis tight