Rune Allnor
Guest
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 Posted:
Tue Dec 20, 2005 1:16 am Post subject:
Re: Question about cross-spectrum and convolution |
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Ze Ji wrote:
| Quote: | 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)
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Here "*" means convolution, right?
| Quote: | Isn't it the same as:
FT(X) FT(Y)
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No. The cross spectrum is defined as
FT(X) x conjugate(FT(Y))
where "x" means multiplication.
| Quote: | My simple clue is:
X*Y = IFT( FT(X) FT(Y) )
So, FT(X*Y) = FT(X) FT(Y).
Am I right?
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Except for the conjugate:Yes, you are right. It is not very difficult
to work out the details. Most intermediate-level texts on DSP
contain a chapter named "Properties of the Fourier Transform"
where this is one of the standard derivations.
Rune |
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