how to generate an abitrary length colored noise when the PSD is know !

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I want to generate colored noise samples of arbitrary length, I have the PSD of the noise in a vector of 512 elements !
Bjorn Gustavsson
Bjorn Gustavsson on 7 Oct 2014
Presumably your signal is then bandlimited to frequencies corresponing to your 512-samples wide PSD, meaning that the PSD at higer frequencies is zero - so you should be able to simply pad the PSD with zeros up to the desired length.

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Answers (2)

Image Analyst
Image Analyst on 20 Aug 2014
You need to use inverse transform sampling. By doing that you can get any distribution you want from a uniform distribution. See
I've also attached a demo where I pull random values from a Rayleigh distribution. Feel free to modify it.
Bjorn Gustavsson
Bjorn Gustavsson on 7 Oct 2014
That would lead to a random-number sequence with a given probability distribution function, but the OP asked for a given power spectral density, as far as I understood the question.

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Youssef  Khmou
Youssef Khmou on 21 Aug 2014
You proceed using Inverse Fourier transform , here is how you can start , let us consider zero mean random variable of length 200 :
f=fft(x); % Discret Fourier Transform with same length
p=f.*conj(f); % Power
figure; plot(p)
C=real(ifft(f)); % inverse transform of the power
figure; plot(C,x) %
the original signal or the ones resulting from inverse transformation are similar, so suppose you have vector of Power spectrum, you ifft with the desired length N :

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