[TubInPlasma]

Hi all, I have recently started working on something related to turbulence, the problem I am working on is two dimensional, I have implemented to compute the energy spectrum E(k) in space, but for some reason I have to compute E(t) in the time domain, and after consulting the relevant sources, I now understand that
E(t) = FFT(<v(t)v(t+τ)>).
I have some questions about the algorithm.
1. i need to get the time series of velocity and compute its autocorrelation function and then FFT it to get E(t), right?
2. my velocity has two components, I try to do a fast Fourier convolution on each component and then add the results of the two components to get their autocorrelation function
3. I have reviewed several papers and found that their general idea is basically to do an FFT on the autocorrelation function for positive time delay and then get the power spectrum, but I have used test data to test my existing code and I don't seem to get the correct results, what is the problem?
Any answer would be appreciated!