Power spectrum for real, imaginary and complex functions.

[hahashahid]

Homework Statement

What can we say about the evenness and oddness of the power spectrum (|F(s)|[itex]^{2}[/itex]) if the input fuction is purely real, purely imaginary or complex?

I know that a real function will give an even power spectrum. But I can't prove it!

Homework Equations

F(s) = A(s)e[itex]^{j\Phi(s)}[/itex]
|F(s)|^2 = F(s).F*(s)

The Attempt at a Solution

I'm stumped!

 

[clamtrox]

Power spectrum involves Fourier transformations right? You might be able to make some progress if you look how the complex conjugates of FT's simplify, depending on reality of the transformed function.