[SciPy-Dev] 1/f noise generation

[Neal Becker]

good point!

On Fri, Aug 11, 2017 at 4:55 PM Nathaniel Smith <njs at pobox.com> wrote:

> On Wed, Aug 9, 2017 at 10:19 PM, Phillip Feldman
> <phillip.m.feldman at gmail.com> wrote:
> > Firstly, white noise means only that the power spectral density is flat,
> or
> > equivalently, that the autocorrelation function is zero everywhere
> except at
> > lag zero.
> >
> > One can generate Gaussian noise with an arbitrary power spectral density
> by
> > filtering white Gaussian noise with a suitable filter. The output of the
> > filter is the convolution of the impulse response of the filter with the
> > autocorrelation function of white noise, which gives us the impulse
> response
> > of the filter. So, from the convolution theorem and the definition of the
> > PSD, the PSD of the output is the squared magnitude of the frequency
> > response of filter.
>
> It's not actually possible to generate true 1/f noise this way --
> technically 1/f noise is non-stationary and doesn't have a PSD. (You
> can run a PSD estimator on any finite sample of 1/f noise, and get
> some answer, but as your samples get larger your estimate won't
> converge, because you keep discovering more and more power at lower
> and lower frequencies.) So there are specialized methods for
> generating 1/f noise, involving things like fractional differencing or
> wavelets.
>
> -n
>
> --
> Nathaniel J. Smith -- https://vorpus.org
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