Dear Dick,
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.
Regards,
Randy Randhawa
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
frequencies).
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"?
Dick