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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
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
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