Fourier transforms of power of a function

[sumesh.pt]

I am not able to comprehend this :
/int dx (df(x)/dx)^2 = \sum (q^2 F(q)^2 where F(q) is the Fourier transform of f(x).

Can some one throw light?
thanks.

 

[cepheid]

I'm typesetting your attempt at LaTeX properly so that I can read it:

I am not able to comprehend this :
$$\int\, dx \left(\frac{df(x)}{dx}\right)^2 = \sum q^2 F(q)^2$$

where F(q) is the Fourier transform of f(x).

Can some one throw light?
thanks.

 

[cepheid]

I don't think that the equation, as it stands, is true. It's also not very clear because you haven't specified what range you are summing over on the right-hand side. If you told me that the Fourier transform of what was on the left-hand side was equal to the right-hand side, I might believe it. Because you mentioned the power of signal, I suspect that this might be a combination of Parseval's relation for Fourier transforms (or series?) and the differentiation property of said transform (or series).

 

[sumesh.pt]

Thanks for the reply.
In RHS summation is over all possible q. Could you please clarify the last part of your explanation where you say that it would be true if it is written as FT(LHS) and use a combination of Parsevals theorem and some differentiation property. How do I see that?
Thanks.