Is there a code to get multiple velocity time histories equivalent to a single power spectrum?

I am working on generating seimic noise numerically. I have a power spectrum (power spectral density). I want to generate velocity time histories compatible to the power spectrum. Is there any code for that?

Answer 1

[Maneet Kaur Bagga]

Hi Ankit,

As per my understanding, to generate velocity time histories compatible with a given power spectrum "Fourier Amplitude Spectrum Method" can be applied which involves the following steps:

• Define the desired power spectral density (PSD) function or curve. Convert the PSD to a one-sided amplitude spectrum by taking the square root of the PSD values.
• Generate a random phase spectrum with random phase angles between 0 and 2π for each frequency component.
• Combine the amplitude and phase spectra to obtain the complex spectrum.
• Perform an inverse Fourier transform on the complex spectrum to obtain the time-domain signal.
• Apply appropriate scaling factors, to match desired units and amplitude.

For code reference please access the below File Exchange Link:

https://www.mathworks.com/matlabcentral/fileexchange/70166-compute-smooth-fourier-amplitude-spectrum-smoothfas

Hope this helps!