I am learning about generating Gaussian random fields by spectral simulation...
If I have a covariance function $C(h)$, then the spectral density is the Fourier transform of $C(h)$:
$S(\omega)=(1/N)\sum_{h=0}^{N-1}{C(h)[cos(2\pi\omega h/N)- i \sin(2\pi\omega h/N)]} \space\space\space\space\space [w=0,...,N-1]$
So, obviously there is are real and imaginary parts to the spectral density. Then, I take the square root of the spectral density to get the amplitude spectrum:
$|A(\omega)|=\sqrt{S(\omega)}$
So, there should also be real and imaginary parts of the amplitude spectrum too right?
I have been using a program called SPECSIM2, which I downloaded from here.
Using this program, (or another like ImageJ), I can plot the amplitude spectrum... Is that just taking the real component of the amplitude spectrum then? Is the imaginary component known as the phase spectrum?
