psd2timeseries

[Eta, t, Hm0, fp, fEta, SxxEta, a] = psd2timeseries(f, Sxx, fs, CalcMethod, dispout)

Description

Generate random wave data from a given spectrum

Inputs

f

Frequency (Hz)

Sxx

Power spectral density (m^2s)

fs=8;

Sampling frequency that data collected at in (Hz)

CalcMethod=’fft’;

Method for Calculating random time series,

‘fft’: using Fast Fourier Transform, ‘sp’: using wave superposition

dispout=’no’;

Define to display outputs or not (‘yes’: display, ‘no’: not display)

Outputs

Eta

Water Surface Level Time Series in (m)

t

Time in (s)

Hm0

Zero moment wave height (m)

fp

Peak wave frequency (Hz), fp=1/Tp (Tp: Peak wave period (s))

fEta

Frequency from generated time series(Hz)

SxxEta

Power spectral density from generated time series (m^2s)

a

Wave amplitude for for one-sided spectrum (0<fEta<fs/2) from generated time series (m)

Examples

N=2^11; %Total number of points
fs=8; %Sampling frequency
df=fs/N; %Frequency difference
f(:,1)=[0:df:fs/2]; %Frequency vector
f(1,1)=f(2,1)/2; %Assign temporarily non-zero value to fisrt element of f to prevent division by zero
Sxx=0.016.*9.81.^2./((2.*pi).^4.*(f.^5)).*exp(-1.25.*(0.33./f).^4); %Calculating Spectrum
f(1,1)=0;
Sxx(1,1)=0;
[Eta,t,Hm0,fp,fEta,SxxEta,a]=psd2timeseries(f,Sxx,fs,'fft','yes');

References

Branlard, E. (2010). Generation of time series from a spectrum. Technical University Denmark. National Laboratory for Sustainable Energy.