Re: Robust method of fundamental frequency estimation.

["Richard F. Lyon" <DickLyon@xxxxxxx>]

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

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.

Dick