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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.