I want to generate white Gaussian noise with known PSD. Using wgn I can generate noise with specific power (dBW) but I want to generate a white noise with constant or know PSD.
Can anyone give me some idea. Thanks Franklin
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2$\begingroup$ The very definition it white noise is a constant PSD... $\endgroup$– Marcus MüllerNov 12, 2017 at 10:04
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$\begingroup$ Could you please mark the answer? Thank You. $\endgroup$– RoyiSep 22, 2022 at 15:22
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1 Answer
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The specific PSD is basically white noise which was filtered with a filter which its Magnitude is the same as the PSD.
This is a result of the Wiener Khinchin Theorem.
So if you have the shape of the PSD do the following:
- Create a filter which in the Frequency domain has the magnitude (More accurately the squared magnitude $ {\left| H \left( \omega \right) \right|}^{2} $) of the PSD you want (Namely, you don't care about the phase).
- Create a White Noise.
- Filter the white noise with the filter created in 1.
I would note that in the case of a White Noise the PSD is constant.
Hence in this case all you need is to generate white noise with normalized variance and then to multiply it by a constant (Changing its variance) to the value you're after.
Enjoy...
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$\begingroup$ In the discrete-time LTI filtering with WSS input $x[n]$ and output $y[n]$, the PSD relation is $$ S_{yy}(\omega) = |H(\omega)|^2 S_{xx}(\omega) $$, so did you mean Magnitude Square instead, that's why you don't care of the phase... Or did you mean another method of noise generation ? $\endgroup$– Fat32Aug 20, 2018 at 15:26
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$\begingroup$ I made it more clear. I indeed meant that (It was abuse of the word magnitude). Thank You. $\endgroup$– RoyiAug 20, 2018 at 15:32