

Re: Robust method of fundamental frequency estimation.

At 9:27 AM -0500 2/27/07, Arturo Camacho wrote:

Arturo, that's funny! Eckard calls you Roberto and you come back calling him Erick. ROFL.

Let me describe my reasoning again with more detail. To facilitate the
explanation let's assume we have infinite length signals and infinitely
narrow filters. Applying the filterbank to the signal leave us with a
decomposition of the signal into its sinusoidal components. Since there is
only one sinusoid per channel, the spectrum at each channel consists of a
single pulse (possibly of zero magnitude) at the central frequency of the
channel. Computing autocorrelation at each channel corresponds to squaring
the magnitude of the spectrum of the signal (a single pulse) and
synthesizing a cosine at that frequency (by Wiener?Khinchin theorem). The
summary autocorrelation just adds those cosines over channels.

This view of the narrowband limit of the filterbank completely misses the actual behavior that good cochlea models capture. The channels are not nearly so narrowband that their outputs can be considered to be even approximately sinusoidal. And there's also a half-wave rectifier at each channel output that you have waved away. Without these, of course the Licklider approach to pitch can not be made to work, nor can its differences from other approaches be appreciated.

I recommend you google up "On the Importance of Time," a chapter that Slaney and I wrote on how these models work. An open issue in this class of models is how best to summarize and pick a pitch from the correlogram; a study like you've done, but applied to this different domain, would be interesting to see.