Question about cross-spectrum and convolution

Ze Ji-

> Hi, I have a question regarding the concept of
cross-spectrum, which is
> defined as the Fourier transform of convolution between two signals X and
> Y:
>
> FT(X*Y)
>
>
> Isn't it the same as:
>
> FT(X) FT(Y)
>
> My simple clue is:
>
> X*Y = IFT( FT(X) FT(Y) )
>
> So, FT(X*Y) = FT(X) FT(Y).
>
> Am I right?

Yes right, and correlation amounts to division in the frequency domain;
i.e. transfer function calculation.  Easy to conceive, but there are lots
of details to actual implemention in a real-time system that operates on
continuous data.

For use of FFT to accomplish frequency domain processing in real-time
systems, here is a good book that takes out the guesswork:

  The Fast Fourier Transform and its Applications
  E Oran Brigham
  ISBN 0-13-307505-2

-Jeff