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Re: On pitch and periodicity (was "correction to post")
While linear system theories seem to work reasonably well with
mechanical systems, I believe they fail when applied to Biological
systems. Consider that even Helmoholtz had to appeal to non-linear
processes (never really described) in the auditory system to account for
the "missing fundamental" and "combination tones". Both of these
psycho-acoustical phenomenon have been well established and explanations
for pitch perception are either spectral based or time based with some
throwing in learning and cognition to avoid having to make the harder
decision that maybe this field needs a new paradigm. This new paradigm
should be able to provide a better model that explains frequency
(sound!) analysis in a fashion such that the nothing is missing and
parameter values can be calculated to explain pitch salience, a subject
that seems to be never discussed in pitch perception models.
Furthermore, such a new approach should also be able to explain why the
cochlear is the shape it is, which as far as I can see has never been
touched upon by existing signal processing methods. Finally, are these
missing components "illusions" that are filled in so to speak by our
higher level cognitive capabilities? It is remarkable that this so
called filling in process is as robust as it is, to be more or less
common to everyone, and therefore one wonders if all the other illusions
are really not illusions but may have a perfectly good basis for their
existence. If they were "illusions" one would expect a fair amount of
variation in the psycho-acoustic experimental results I would think.
I myself gave up on linear systems early in my study of this field and
have felt that other systems, e.g. switching, may offer a better future
explanatory capability, especially when it comes to showing some
commonality of signal processing between the visual and the auditory
system. To this end, I am quite happy to accept that I do not consider
myself an expert in linear system theory.
On 8/2/2011 1:49 PM, Richard F. Lyon wrote:
At 5:55 PM +0300 8/2/11, ita katz wrote:
The periodicity is determined by the least-common-multiple of the
periodicities of the present harmonics, so if (for example) a sound
is composed of sines of frequencies 200Hz, 300Hz, and 400Hz, the
periods are 5msec, 3 1/3msec, and 2.5msec, so the
least-common-multiple is 10msec (2 periods of 5msec, 3 periods of
3.33msec, and 4 periods of 2.5msec), which is of course the
periodicity of the sum of the sines, or in other words 100Hz.
(actually it is the same as the greatest-common-divisor of the
Ita, that explanation is sort of OK, but as written implies that the
auditory system has the ability to do number-theory operations on
periods (or frequencies), and depends on there being harmonics present
and separately measureable.
It would be much more robust to say that "The pitch is determined
based on an approximately common periodicity of outputs of the
cochlea," which I believe is consistent with your intent.
Why is this better? First, it doesn't say the periodicity is
determined; what is determined is the pitch (even that is a bit of
stretch, but let's go with it). Second, it doesn't depend on whether
the signal is periodic, that is, whether harmonics exist. Third, it
doesn't depend on being able to isolate and separately characterize
components, harmonic or otherwise. Fourth, it doesn't need
"multiples" (or divisors), but relies on the property of periodicity
that a signal with a given period is also periodic at multiples of
that period, so it only needs to look for "common"
periodicities--which doesn't require any arithmetic, just simple
neural circuits. Fifth, it admits approximation, so that things like
"the strike note of a chime" and noise-based pitch can be
accommodated. Sixth, it recognizes that the cochlea has a role in
pitch perception. It's still not complete or perfect, but I think
presents a better picture of how it actually works, in a form that can
be realistically modeled.
Is this "tortured use of existing signal processing techniques" as
Randy puts it? I don't think so. Is it "a unique way to do frequency
analysis and to meet the dictum in biology that 'form follows
function'"? Sure, why not? But why call it "frequency analysis"?
How about "a unique way to do sound analysis" (if by "unique" we mean
common to many animals)?
I do have some sympathy for Randy's concern that we are far from a
complete understanding, and that hearing aids are not as good as they
would be if we understood better, but yes, he sounds way too harsh in
overblowing it so. I'm wondering what's behind that, and whether it's
just confusion about all the confusing literature on pitch perception,
which I agree is a complicated mess -- or is the problem, indicated by
Randy's previous posts, just that he doesn't understand basic linear
systems and signal processing, and that's why it all seems "tortured"?