# Re: [AUDITORY] pitch ("Alain de Cheveigne'" )

```Subject: Re: [AUDITORY] pitch
From:    "Alain de Cheveigne'"  <alain.de.cheveigne@xxxxxxxx>
Date:    Thu, 17 Oct 2013 10:20:37 +0100
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

Here's the recipe:
(1) estimate the period with subsample resolution (e.g. with Praat or =
YIN),
(2) interpolate the signal over a period interval to an integer number =
of samples,
(3) apply the Digital Fourier Transform (DFT).

The coefficients of the DFT give the amplitude and phase of each =
harmonic.  These values are exact if the signal is purely periodic.

Optionally, if the signal is noisy, you might want to average the =
complex DFTs of several periods (or equivalently, average the waveforms =
of the periods before applying the DFT).  Alternatively, you might =
prefer to average the power spectra of those periods, and take the =
square root to get the RMS amplitude spectrum (similar to the Welch =
method).   The choice between these two options depends on which aspects =
of the non-stationary signal you want to average out.

The period interval signal is not windowed before the DFT.  If speed =
were an issue you might interpolate to a power of two and use FFT to =
calculate the DFT.  Various methods are available for interpolation, the =
best choice depends on your exact needs.  For a first approximation, =
simple linear or quadratic interpolation might suffice.

Alain

On 16 Oct 2013, at 15:16, herzfeld <herzfeld@xxxxxxxx> wrote:

> Can anyone point me to a method which takes as input a signal having a =
number of harmonics and computes each harmonic as frequency, amplitude =
and pitch even in the absence of some of the partials ?
>=20
> Fred
> -------------------
>=20
> Fred Herzfeld, MIT class of 1954
> 78 Glynn Marsh Drive # 59
> Brunswick, Ga. 31525
> USA
>=20
> tel: (912) 262-1276
> Web: http://alum.mit.edu/www/herzfeld (not up yet)=20
```

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Electrical Engineering Dept., Columbia University