Re: Autocorrelation

[Peter Cariani <peter@xxxxxxxxxxxxxxxxxxxx>]

Christian Kaernbach wrote:
> Please forgive me that I will not enter into this discussion in this
> detail. Whenever my daily e-mails takes me more than 10 minutes I am
> convinced something is going wrong. My only and major point was and is:
> K&D 1998 is important to modelers because it sets constraints (asymmetry
> of 1st- and 2nd-order regularities). Up to the modelers to show that
> there is no problem. And I am not interested in comments why this and
> that model fails to reproduce this asymmetry (neglecting tails of tunig
> curves or whysoever).... all this is pure speculation. I am interested
> in models that succeed to produce this effect.

I would not want to waste any more (than 10 minutes) of your time
regarding these  broader issues, which involve the neural substrates of
auditory percepts that encompass phenomena other than the masking of
these click trains that are produced by psychophysically-unresolved
harmonics.

Jont Allen wrote:
> How do the tails become involved? The levels would need to be  very large, wouldnt they? Also the neural filter would emphasis the tip region, so the spikes envelope would depend mainly on the cf region.

At 60 dB SPL a harmonic complex consisting of harmonics below 1 kHz will
 impress the periodicity of its fundamental on fibers whose CF's are
2-10 kHz. These fibers may not fire at rates much higher than
spontaneous, but their discharges are locked to the stimulus
fundamental, so they contribute pitch-related intervals to the global
interval distribution. Whether responses will be dominated by components
near or far from CF will depend on their relative intensities, and also
potentially on temporal precedence patterns.

I brought up tails of tuning curves initially, because the
population-interval representation is the distribution of all-order
interspike intervals across the whole auditory nerve array, and that
lower-frequency components at moderate levels effectively drive
higher-CF fibers, which then contribute pitch-related intervals to the
distribution as a whole. This is one (temporal) way of thinking about
the upward spread of masking -- when one sums all of the intervals from
lower frequency and higher frequency components, because of the
asymmetry of tuning curves and better phase-locking to lower
frequencies, more intervals related to the lower component  are
produced. The broadening of tuning curves means that a global interval
representation can make use of the full dynamic range of the whole
auditory nerve array -- the extent of a given temporal pattern spreads
with higher level. The tails of tuning curves come into the present
discussion partly because K & D used low-pass noise, and this low-pass
noise also has the effect of masking the pitch produced by higher
partials, thereby lowering its salience and making the task more like a
pitch detection near threshold rather than the masking of a more salient
pitch well above threshold (but as I said before, the more general
masking result is quite robust and striking in the absence of the LP
noise and well above threshold).

If you don't factor in the tails and the low-pass noise nor the stronger
degree of phase-locking to lower frequency components, as K & D decided
not to do in their simple autocorrelation, then the relative height of
the pitch-related autocorrelation peak is artificially higher than it
would otherwise be. I don't fault them for using the simple
autocorrelation model -- for many purposes, especially for resolved
harmonics as one finds in musical contexts, it is not a bad rough
approximation, and more involved neural models introduce all sorts of
additional factors and distract from K & D's primary interest, which is
in the psychophysics. However, if one knocks down a simple model (that
nobody believes literally) for a limited range of
high-frequency/harmonic number masking phenomena  (that, in themselves,
are relatively unimportant as far as pitch perception goes), one should
not claim that one has falsified an entire theory or whole class of
models. It is exceedingly difficult to rule any model out of hand,
including rate-place-based spectral pattern models for pitch (this is
why definitive experiments in the neurophysiology of perception are few
and far between). I can imagine ways in which spectral pattern
mechanisms might be operant in covert form, even though we have yet to
observe any neural response patterns that would support such analytical
mechanisms. All models need to be kept on the table, in their strongest,
most plausible forms, and all possibilities need to be considered.

In any case, we don't throw out the Copernican model because we observe
that the orbits are ellipses not circles, and that the sun is not
exactly at the center of the solar system. One doesn't go back to
epicycles (or to spectral pattern mechanisms) because of such
observations; one refines the models.

-- Peter Cariani