From Complex Fourier Co-efficients to time series


I am interested in constructing a model of LLJs that occur offshore. As a starting point, I am looking to generate turbulence via the Sandia/Veers method. As such, I am in the process of writing a Matlab script. I am forming a new spectral matrix, coherence matrix, H matrix etc. for each frequency. That is, the spectral matrix, coherence matrix, and H matrix are all N-by-N matrices where N is the total number of points on the grid (N = Ny*Nz). I have checked what my Matlab script is doing and it seems to be sensible up to that point. I am then operating on the H matrix with a vector containing white noise (N-values). This gives me the complex Fourier co-efficient for each point on the grid at the frequency being examined at that point. The script then runs through the entire frequency range so that all the complex Fourier co-efficients for all points across all frequencies is known. Is my understanding of the Veers method correct up to this point? If so, my problem is that I can’t figure out how to take this data and get the time series. What do you need to do with the complex Fourier co-efficients for each point to get the time series of the turbulence at said point?

Many thanks,