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How to generate a time signal from spectrum

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Alessandro Antonini
编辑： Walter Roberson 2024-8-9，19:05
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.

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回答（2 个）

Abhishek Ballaney
编辑：Walter Roberson 2024-8-9，19:05
Isaac
Isaac 2024-8-9，18:15
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

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