FFT of sine wave shows unexpected spectral widening

Trying this code:

res = 1024;

t = 1:res*90;

t = t/res;

FreqList = [ 0.1, 0.25, 0.5, 0.55, 1];

templeS = (10*sinpi(2*FreqList(1)*t));

for i = 2:numel(FreqList)

templeS=templeS+(10*sinpi(2*FreqList(i)*t));

end

ff = fft(templeS);

frq = 0:numel(t)-1;

frq = frq*res/numel(t);

figure;

plot(frq, abs(ff));

xlim([0,1.1]);

I expected to get sharp peaks at FreqList. However....

Can anyone explain this stange behavior of 0.25 and 0.55 frequencies?

BTW, i tryed also 0.24 and 0.56 without other frequencies, as well as different resolutions, with the same effect os spectral widening...

Answer 1

[Bjorn Gustavsson]

Try this:

subplot(1,2,1)
plot(templeS)
axis tight
ax = axis;
axis([[-30 0]+ax(2) ax(3:4)])
subplot(1,2,2)
axis tight                      
plot(templeS)
axis tight
ax = axis;
axis([[0 6000]+ax(1) ax(3:4)]) 

Then you'll see that the function might be continuous around at the boundary, but its first derivative is not. Therefore the spectral widening. If you try the to select a period where your signal is nicely periodic you get much nicer peaks:

ff2 = fft(templeS(1:(89600)));

HTH

[Eli Ratner]

Thanks, but i get widening at other frequenciesi in this case. Of course, i can find the number of samples for complete period of all used frequencies, but it seems me incorrect way to work with real signals...

Indeed, i expected that the error of not whole cycle will be much smaller, because the number of cycles is large enough...