FFT not working on periodic data!?!?!?

Hello,

I have data which, when visualized,, displays some very periodic behavior (picture a 2D sine wave). However, when I call the fft2() function on my matrix I only get the zero-frequency bin to be non-zero. I would have expected the very clear periodicity in my data to become clear in the FFT, but it seems that somewhere something's going wrong!

Any ideas, including common mistakes or misunderstandings with fft2 or FFTs in general?

Actually, it's quite weird that, regardless of my data, I only get the zero-frequency bin lighting up in the fft!!

code: (msum2 is my real data)

zMapT2=fftshift(fft2(msum2));

zMapAbs=abs(zMapT2);

imagesc(zMapAbs);

so I'd expect to see some bins lighting up away from the origin, but everything's blue except for the red at the center.

[Rick Rosson]

Please post your code.

[Rick Rosson]

Please type the following at the command prompt:

   mean(msum2(:))
   min(msum2(:))
   max(msum2(:))
   size(msum2)
   class(msum2)

What is the value of each of these expressions?

[Bruce]

mean:23.4562

min:21.5823

max:27.5662

size:256 256

class:double

Answer 1

[Image Analyst]

See my attached demo.

Can't really say much about your code since you didn't post it all. It might be that you have the signal on a big offset, like the signal is all positive, so that there is a huge DC (zero frequency) term which is so much bigger than your spikes due to your periodic component that you can't see the spikes due to the periodic part. You might try taking the log of your data before you pass it to imshow() or imagesc().

[Image Analyst]

It could also be that your colormap is such that it hides your spikes. Try using

colormap(gray(256));

instead of the weird colormap that imagesc() uses.

[Bruce]

Thanks for your ideas. I tried changing the figure colormap as instructed, but now I just get one white center dot in a sea of black. I also tried doing decibel scaling, to no avail!

msum3=10*log10(max(1,msum2));

proceeded as before, still one lone dot!

See my comment to Rick above - my data doesn't seem that wildly varied, and it doesn't have a huge spike somewhere (right?). So confused - seems so straightforward, can't think of why this particular data set is having issues.

[Image Analyst]

Unless you post your actual data I don't know how much more help we can give.

Answer 2

[Rick Rosson]

Please try converting the source data to zero mean before taking the FFT:

   mu = mean(msum2(:));
   msum2 = msum2 - mu;

That will eliminate the DC component, and it should reveal the periodic components in the Fourier domain.

[Bruce]

This did it! Thank you Rick! I'll have to do more research to understand why this worked.

[Bruce]

Can't find a way to accept your answer though...

[Image Analyst]

It looks like you didn't take the log correctly when you tried to take my suggestion. You took the log of the time or spatial domain instead of the Fourier/spectral domain. Anyway, done correctly, taking the log before plotting/displaying will compress the DC spike and give the little spikes a chance to be seen. Of course if you don't want the complete spectrum and want only the little periodic spikes, then just get rid of the DC spike by subtracting the mean like Rick suggested.

[Bruce]

I see. I'll try what you said again, thank Analyst!

[Bruce]

Yes, that worked too! They are different images, but the peaks I was after are present in both. I can see the difference between removing the DC spike and just compressing it - very interesting! Thank you both very much for your time. -Bruce