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I have a white noise signal that I plot on a log(PSD) vs log(frequency) plot. Now I want to filter that signal with several different filters to to get different alphas (0.5 to 3.0) in the 1/f^alpha sense. I'd like to use the same filter but get different alphas based on the filter parameters. Each log(PSD) vs log(Frequency) plot should be as linear as possible over a wide frequency range. I am assuming that some filter will provide this. I need a filter that will produce several alphas near 0.5, 1.0, 1.5, 2.0, 3.0. Maybe filtering is not the way to go. Need help.

Lee Friedman
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  • I use an FFT approach for arbitrary phase noise profiles that someone had worked out the details for on Matlab’s file exchange site and which I ported to Python- would the details on that help you? With that you can generate noise waveforms with any arbitrary slope including breakpoints. – Dan Boschen Apr 22 '22 at 14:34
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    Maybe look at the answer here and the other answers there as a start. – Ed V Apr 22 '22 at 14:53
  • Thanks Dan and Ed. As you are aware, as the intensity of filtering increases the temporal autocorrelation increases. I need the 1/f^alpha types to have larger autocorrelations as alpha also goes from 0 to 3 or so. I will give your solutions a try. – Lee Friedman Apr 22 '22 at 15:16
  • Yes, Ben. I am a Matlab user so a file from mathworks file exchange would be very useful. – Lee Friedman Apr 22 '22 at 15:19
  • Here is the Matlab link but I think Ed’s link is better for cases when a fixed slope is sufficient https://www.mathworks.com/matlabcentral/fileexchange/8844-phase-noise – Dan Boschen Apr 22 '22 at 15:34
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    Does this answer your question? Pink ($1/f$) pseudo-random noise generation – lennon310 Apr 22 '22 at 15:35
  • I got Ben's solution working. It uses https://www.mathworks.com/matlabcentral/fileexchange/8844-phase-noise. Had to modify it for my specific application but got it working in short order. One issue: it produces 1/f noise for most of the frequencies but at the very end, it shoots up to a high level again. Is this expected? Can this be prevented> – Lee Friedman Apr 23 '22 at 22:05
  • That is, starting at about 245 Hz of a maximum 500 Hz, the curve turns up and at the very high end spikes upward. – Lee Friedman Apr 23 '22 at 22:09
  • I would post an image from my computer but I can't figure out how. I have 31 reputation points. – Lee Friedman Apr 23 '22 at 22:17

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