The question is pretty self explanatory. I want to know if it is possible to recover a signal originally injected into noisy data (coloured gaussian noise) after whitening the data with an AR minimum phase filter. I want to recover the phase.

  • $\begingroup$ I think yes - minimum-phase filter is inversible, if you know the filter coefficients. $\endgroup$
    – ZR Han
    Jan 31, 2023 at 10:45
  • $\begingroup$ Please elaborate on what you mean by “recovered” (perfect recovery or an estimate) and if you have more details on the spectrum of the colored noise. $\endgroup$ Jan 31, 2023 at 16:04
  • $\begingroup$ probably meant deconvolution $\endgroup$ Jan 31, 2023 at 20:11
  • $\begingroup$ @DanBoschen I have data with gaussian colored noise n(t). The PSD of n(t) is the sum of multiple components (pink, brown, noise lines and whatever). A typical detector with different noise sources. The signal s(t) can be a chirp, sine gaussian or any short transient. After applying a whitening filter W(t), to remove correlations in the data and obtain white noise background, my signal s'(t) will differ from the original one, since it passed through the minimum phase filter. I want to know if I can obtain s(t) or an estimate from the whitened time series. I want to preserve the phase of s(t). $\endgroup$
    – GWSurfer
    Feb 1, 2023 at 17:30
  • $\begingroup$ The filter is of course invertible as ZR Han suggested, but doing that would just get you back to the signal as it existed before the filter (which doesn't sound like what you want). I suspect the solution may be similar to this post but would need to think that through in more detail. Hopefully @MattL sees this and can comment further on its applicability. dsp.stackexchange.com/questions/37902/… $\endgroup$ Feb 2, 2023 at 14:26


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