Autocorrelation

[Christian Kaernbach <chris@xxxxxxxxxxxxxxxxxxxxxxxxxx>]

Peter Cariani wrote:
> As far as objections to population-interval representations go, the
> conclusions of Kaernbach and Demany should not be taken at face value

Dear Peter,

I am so sorry I have not the time to follow these interesting but
lengthy discussions in detail. Let me point out shortly in answer to
your comments on our paper:

> 1) The "autocorrelation" model that they knocked down was not neural
> model; 

It would be difficult to knock down all possible neural autocorrelation
models. Our experiment gave a hint that there might be a problem with
higher-order regularities which are seen by autocorrelation, but not by
perception. I did not see a contribution up to now where somebody showed
that neural autocorrelation would produce this asymmetry between first-
and higher-order intervals. We supplied some modelers with our stimuli,
and they could not make their models produce this asymmetry.

> 2) The stimuli were harmonic complexes whose harmonics (F0=100 Hz)
> were all above 5 kHz

In our new submitted paper (you should know of it) we are down to 2 kHz,
and the asymmetry is just the same. It is a real problem to go down much
lower, as one should exclude frequencies lower than 15 times the
fundamental. You did not specify whether in your below-2-kHz click
trains resolvable harmonics were excluded (and masked for distortion
products). In our understanding, it is not the frequency region but the
resolvability that counts.

> 3. K & D assumed that each of their clicks would give rise to a spike
> in an auditory nerve fiber.

Not precisely so. We only assumed that _most_ of the inter-spike
intervals on the auditory nerve would correspond to inter-click
(inter-stimulus) intervals. But this assumption is not crucial to our
argument. Please let me cite from our General Discussion section:

    It is plausible that the ‘‘final’’ temporal structure contributing
    to pitch sensations (either directly or after a conversion
    into a place code) does not occur in the auditory nerve
    but at a higher location in the auditory system. We believe
    that at this stage the ISIs that matter are first-order ISIs.
    However, the consecutive spikes bounding these ISIs may
    originate from nonconsecutive spikes at the auditory nerve level.

> 5. In short, lower frequency hearing has more autocorrelation-like
> qualities (intervening clicks don't mask much; ...),
> while high frequency hearing has more modulation-like qualities
> (intervening clicks mask, ...).

Again, IMHO it is resolvability that counts. When I asked at the ASA
meeting in Berlin what could be a generally accepted boundary between
low- and high-frequency regions I was pointed to the 4 kHz boundary
where neural phase locking ends. With our new publication we are well
beyond this limit (i.e. intervening clicks mask in stimuli starting at 2
kHz). On the other hand, it is a very simple demonstration that
intervening clicks don't mask in the high-frequency region AS LONG AS
THERE ARE RESOLVABLE HARMONICS.

I hope this clarifies. Sorry to be lengthy. It will not happen again...

Christian