How to generate a time signal from spectrum

Hello,

I'm working on spectrum comes from sea wave data. I have a JONSWAP spectrum and I need to generate a signal in time domain to fed my numerical model of a floating body, can anybody suggest me how do it.

[Mirlan Karimov]

If you could get any result please share it with me via [e-mail] I am working on the same problem

Answer 1

[Abhishek Ballaney]

https://in.mathworks.com/help/matlab/ref/ifft.html

Answer 2

[Isaac]

If you have a power spectral density function (PSD), and not a fourier series of the Jonswap then you can't just take an ifft of the spectrum because it is a measure of energy of a frequency band (m^2/Hz), and it no longer has any phase information.

This function will generate a timeseries from a PSD based on equations 8 and 9 in Tabeshpour, 2023. It uses the rand() function to add back in phase, so it will generate a different result each time it is run. If you require preserveing a time series, you can save the rand seed in MATLAB by using rng() (see https://www.mathworks.com/help/matlab/ref/rng.html?searchHighlight=rng&s_tid=srchtitle_support_results_1_rng)

function [t,wave] = PSD_Time(df,Sj)
% Method derived from: 
% Tabeshpour, M. R., & Belvasi, N. (2023). Ocean waves 
% time-series generation: minimum required artificial wave time-series 
% for wave energy converter analysis. Journal of Marine Engineering & 
% Technology, 22(6), 273–283. https://doi.org/10.1080/20464177.2023.2197280

l=length(Sj);
t=linspace(0,df^-1,l);%generate output time vector
di=rand(1,l)*2*pi;%random phase angle generation

wi=[df:df:df*l]*2*pi;%Angular frequency
ai=sqrt(2*Sj*df);%Cos wave amplitudes
ni=ai.*cos(wi.*t'+di);%Matrix of all Cos waves

wave=sum(ni,2)';%Add Cos waves together
end