How can I filter white noise to obtain signal with desired PSD?

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Adam Nieslony
Adam Nieslony on 23 Jan 2015
Answered: Jeremy on 27 Jan 2015
I need to generate various of signals with different PSD (power spectral density) and PDF (probability density function). My input data are only shapes of this two functions and my idea is to generate random numbers of given PDF and after that I will filter the data to signal with desired PSD. It is no problem for me to obtain the random numbers. I am asking only for the filering to desired PSD.
Any tips are welcome.
Regards, Adam

Answers (2)

Jeremy on 26 Jan 2015
you are trying to generate a time history with a specified spectral content, such that a PSD from the output will match the initial specified PSD?
The best way to do this is to interpolate the specified PSD down the bin width and Nyquist frequency that corresponds to the desired record length and sampling rate. (for example 0-2500 in .01Hz bins for a 100s record with 5kHz sampling rate) You will then need to randomly generate the phase spectra, convert to the the real and imaginary components and process with an inverse fft.
Youssef  Khmou
Youssef Khmou on 26 Jan 2015
I think you have to apply a function on abs(PSD) to obtain the desired shape, after applying fft on drawn input x from chosen PDF.

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Jeremy on 27 Jan 2015
If you randomize the phases you will end up with a Gaussian distribution because the magnitude at every point will be a random combination of so many different signals. I don't have a real good theoretical explanation, but I have done it and if the phases are randomized you have signal that looks very random and it will have a gaussian distribution as the PSD goes to a constant value.

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