> 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)
Here "*" means convolution, right?
> Isn't it the same as:
>
> FT(X) FT(Y)
No. The cross spectrum is defined as
FT(X) x conjugate(FT(Y))
where "x" means multiplication.
> My simple clue is:
>
> X*Y = IFT( FT(X) FT(Y) )
>
> So, FT(X*Y) = FT(X) FT(Y).
>
> Am I right?
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
Reply by Ze Ji●December 19, 20052005-12-19
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?
Thanks