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Re: Robust method of fundamental frequency estimation.

Anssi Klapuri wrote:

Based on my experience with the multipitch detection of musical
sounds, I would suggest the following:
- -At low pitch values, autocorrelation- or comb-filter
  related methods are better than spectral methods.
  This is because the F0 resolution of the ACF is much better
  than that of FFT at low frequencies. You may check this by
  calculating the F0 difference between two ACF lags at low-pitch
  lags and the frequency difference of two FFT bins at low frequencies.

I would not challenge the assertion that autocorrelation methods outperform spectral methods at low pitches. It would surprise me very much, but I defer to the greater experience of others in the area of f0 tracking.

I would point out however that this argument is a bit of a straw man. Any serious use of frequency information from short-time Fourier spectra has to include some sharpening in the frequency dimension. I use time-frequency reassignment for this purpose, but there are other simpler methods that work too, such as the parabolic interpolation method described by Julius Smith and Xavier Serra.

These do not improve the resolving power of the spectrum (and in this way, the multipitch problem is quite different from the estimation of the pitch of a single instrument tone), but they do improve the precision of the frequency estimates you can obtain from the spectrum data, and any comparison of the two domains has to include this extra sharpening step.

-Kelly

p.s. fwiw, I have recently seen a paper (don't know if it is in print yet) that made such a comparison and found that f0 tracking using reassigned spectral data outperformed the autocorrelation method. I cannot recall the details of the autocorrelation method that was used.



--
Kelly Fitz, DSP Research Engineer
Starkey Hearing Research Center