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Re: Non-linear additions to linear models. (was On pitch and periodicity (was "correction to post"))

Hello Randy,

I think you are totally correct in your belief that a new paradigm for
auditory perception is needed.

This thread, which began with a question on how auditory illusions
might affect hearing aid operation, has missed the main point. In my estimation
the greatest auditory illusion of all is that the ear operates by spectrum

To Ohm and Helmhotz the Fourier transform was a mathematical delicacy that
they could use to justify any observation of tonal perception. Since then,
researchers have followed their lead by cherry-picking "ineresting problems"
and proposing solutions involving impressive Fourierian mathematics but
always ending with ineffective, qualified results. There is now not even the
slightest hint of an applicable auditory model.

The reason for this stalemate is that there has been no complete system
analysis to establish the functional and physical requirements for a way to extract
meaning from environmental sounds.  Why else could it be that all animals
have some kind of sonic perception? And, in terms of biological survival,
speech and music would be at the bottom of the list. Yet, with us, these are,
and have been, the primary goals of auditory research.

An analysis of auditory requirements should reveal that there is no physical
way that a spectrum analyzer can respond to the temporal, spatial, and
physiological requirements that are easily accomplished by the ear-brain
system. Given that our ears do things that cannot be done in the Fourier
paradigm, it is only logical that a different paradigm can be discovered:
one that can explain those baffling psychophysical illusions without having
to make wild assumptions.

Good luck,

John Bates

----- Original Message ----- From: "Ranjit Randhawa" <rsran@xxxxxxxxxxx>
To: <AUDITORY@xxxxxxxxxxxxxxx>
Sent: Sunday, August 07, 2011 11:50 AM
Subject: Re: Non-linear additions to linear models. (was On pitch and
periodicity (was "correction to post"))

Hi Dick,
My last observation is on your suggestion of adding non-linearity to some
linear model to cover what some people may call illusions. As an tran
aside, I believe Helmholtz was forced to add in the quadratic function
only because experimentalists (Seebeck I believe) were breathing down his
neck proving the existence of the missing fundamental problem. I would
have to strongly disagree with some of the conclusions reached from such
quadratic and cubic  expansions. In my opinion, I think when people say
that a new paradigm was needed I assumed that it meant a totally new
approach to signal analysis that did not necessarily adhere to any
assumptions of linearity. Take for example a system based on rate of
change of signal  energy, it could right away explain some minor
psycho-acoustic phenomenon associated with changes in static pressure or
that tricky bias term that comes up when one is analyzing sounds like
speech. But as I am sure you would point out, much more would be needed
before such a statement could have any validity as the basis for a system
theory. I agree. On that note, I believe that till some such system is
offered for review, non-linear additions to linear models will have to do
for rest of us who are appalled by the associated mathematics. Regards,
Randy Randhawa

On 8/4/2011 1:42 PM, Richard F. Lyon wrote:

I'll be the first to agree that linear systems theory is sometimes
stretched beyond where it makes sense, and that you need to use nonlinear
descriptions to describe pitch perception and most other aspects of
hearing, and more so when you get up to cognitive levels.

I'm sorry to hear that you "gave up on linear systems", because I don't
think it's possible to do much sensible with nonlinear systems when you
don't have linear systems as a solid base to build on. Certainly at the
level of HRFTs, cochlear function, and pitch perception models, a solid
understanding of linear systems theory is in indispensible prerequisite.
Then, the nonlinear modifications needed to make better models will seem
less "tortured".


At 10:33 AM -0400 8/4/11, Ranjit Randhawa wrote:
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.
Randy Randhawa