I am working with HRIR filters, in particular I am trying to interpolate them. One commod method in the literature to perform interpolation of HRIR is to use the minimum-phase decomposition and interpolate separately the minimum-phase part of the filter and then the all pass part.

You can find more here: https://www.researchgate.net/publication/277879431_On_the_Minimum-Phase_Nature_of_Head-Related_Transfer_Functions

What I am trying to do is to convert my arbitrary HRIR FIR into a minimum phase one. In particular, I am working in Python and I have been using this function.

However while performing the conversion from the original FIR into the minimum-phase one I get the following error:

RuntimeWarning: h does not appear to by symmetric, conversion may fail

With the following code:

min_phase_HRIR_0 = minimum_phase(hrtf[0], 'hilbert')

Where hrtf[0] is a 256 long FIR extracted from a HRIR database (in particular the HUTUBS database).

If I plot the magnitude of my original FIR and the minimum-phase one I get the following plot: Plot

Which is obviously wrong since I am expecting the min phase and the original FIR to have the same magnitude spectrum.

I guess there is something wrong with the Scipy function. Is there anything for Python that converts a FIR into a minimum-phase version?

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    $\begingroup$ The documentation clearly states Convert a linear-phase FIR filter to minimum phase. HRIR are not linear phase and that's exactly what h does not appear to by symmetric means. $\endgroup$
    – Hilmar
    Feb 6, 2021 at 12:40
  • $\begingroup$ Oh, I didn't notice that, my bad. Is there something in Python to compute the min phase version of a FIR? (non restricted to linear phase) $\endgroup$ Feb 6, 2021 at 13:02
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    $\begingroup$ @JuhaP: that would require you to identify poles and zeros first and that's quite difficult with a measured HRIR. $\endgroup$
    – Hilmar
    Feb 6, 2021 at 15:19
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    $\begingroup$ Why wouldn’t a phase linear implementation preserve the magnitude response? $\endgroup$
    – Dan Szabo
    Feb 6, 2021 at 19:15
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    $\begingroup$ Also, I’d be way more concerned about the minimum phase converted magnitude response deviating than I would be a linear phase conversion. $\endgroup$
    – Dan Szabo
    Feb 6, 2021 at 19:44

1 Answer 1


In the end I used the Hilbert transform to compute the minimum-phase phase of my FIR.

I have used the following formula: Formula

Where H is the spectrum of the desired filter.

Which has been used in:

  1. Individualisation d’indices acoustiques pour la synthèse binaurale
  2. Phase Unwrapping for Spherical Interpolation of Head-Related Transfer Functions
  3. Transformation characteristics of the external human ear

However I am not sure of the results I got.

A follow up question discussing the results and implementation can be found here: minimum-phase phase via Hilbert transform returned values

  • $\begingroup$ what is the reference of your formula? $\endgroup$ Jun 25, 2023 at 8:43
  • 1
    $\begingroup$ They're linked in the answer, you can find it in those papers I linked $\endgroup$ Jun 27, 2023 at 12:21

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