Re: The natural spectrogram

[Eckard Blumschein <Eckard.Blumschein@xxxxxxxxxxxxxxxxxxxxxxxxxx>]

At 09:50 30.01.2004 -0600, beauchamp james w wrote:
>Eckard Blumschein wrote (in part):
>>>>Isn't the usual spectrogram subject to the notorious trade-off beween
>>>>spectral and temporal resolution?
>>>
>>>Well sure, but we can let the human ear tell us where to be on that
>>trade-off.
>>
>>This might be not quite correct for several reasons. The smallest product
>>delta t times delta f of hearing is much better than according to the
>>uncertainty principle.
>>Aren't about 10 microseconds and 1 Hz realistic? The product is 10^-5 << 1.
>>Frequency resolution of the natural spectrogram is not at all restricted,
>>in principle.
>
>10 usec and 1 Hz might be JND's for special cases, but I doubt very much
>that they could be discriminated simultaneously. Can you offer an acoustic
>example where they are? In fact, what is the smallest product that has
>been observed, and how does it vary with frequency, intensity, and other
>factors?

Well, you (and also Israel privately) are quite right. I estimated 10 usec
while widespread belief so far erroneously limits the estimation of
bandwidth to less than 20 kHz. The product would equal 0.2 indicating that
temporal accuracy of the front does not correspond to the upper end of the
audible frequency range. There is neither a pertaining limitation to
bandwidth of the signal in the middle ear nor is there a plausible reason
for the basilar membrane to be directly responsible for the 10 usec JND.
Presumably, temporal resolution of a response to a single click is mainly
supported by the bandwidth of the basal turn of cochlea and a high ratio of
auditory nerve fibers per inner hair cell (typically 10, up to 70 in some
bats).
I am sorry, the data are just a wild guess of mine. Please correct me if
delta f = 1 Hz @ 500 Hz takes much more than 400 ms for recognition. A
product 0.4 is smaller than 1 and would also indicate one more hint to the
still astonishing extraordinary perfection of hearing.
When I wrote: 'This might be not quite correct for several reasons' I tried
to evade a detailled discussion as a layman. My only perhaps original
contribution to that issue is the advice that one should not put too much
emphasis on any spectrogram because subsequent neural aspects are at least
equally important. If my gut feeling is correct and we actually perceive
pitch largely by means of joint autocorrelation, then cochlear frequency
analysis is merely the first step, though a decisive one. Maybe, cochlea
adapted to restricted quality of neural systems rather than the other way
round. Width of the CB is clearly not by chance pretty large. The seemingly
poorer spectral resolution, the better is joint autocorrelation.
Those who intend to transfer some excellence of hearing to technical
solutions should first of all try to mimic or outperform the cooperatively
parallelized clever signal processing.

Eckard