I am doing a project on ocean wave simulation and there is a formula I am trying to test. It is called the random coefficient scheme and it is meant to simulate a random time series. One part of the formula is S(f), the 'Energy Density Spectrum'. Here is a screenshot from my notes

The definition I have found for the energy density spectrum is that it is the square of the amplitude of a Fourier transform of a function. That is fine, but I am aware of researchers the EDS to generate virtual waves, and I don't understand what they would use for the value of it there. I imagine it would be reverse-engineered somehow? I am also unsure if it is the same as Energy Spectral Density, a term which seems more common.

I have been reading anything I can find about it but am still struggling to find something I understand. What I want to know is how it is chosen/derived. If i want to simulate my own waves then where could it come from?

I also don't understand how a spectrum is represented in a way that can be multiplied with scalars as required.

Sorry if this is overly specific! I'm not sure what stack exchange site it should be on.


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