Re: Uncertainty principle debate

[Peter Meijer <peter.b.l.meijer@xxxxxxxxxxx>]

Hi All,

John Beerends wrote

> I think the answer lies in the a priori knowlegde,
> if one knows the cycle comes from a long sinusoid
> one can violate the uncertainty relation. The
> uncertainty relation on the cycle itself is maintained.

Yes, roughly speaking, if one has a time window that
contains more sound samples than there are parameters
in a (known) sound generating system, one can solve
for those parameters and seemingly "beat" the frequency
time uncertainty relation even in very complex sounds.
Sounds from additive synthesis are a case in point,
where one has a finite and usually fairly small set
of parameters to solve for the components in a simple
superposition of sinusoidal waves. In fact a very
similar analysis for finite-parameter continuous
time signals, but then applied in a quantum physics
context, is found in the May 2003 article by Zbyszek
Karkuszewski (quant-ph/0304206)

   Harmonic inversion helps to beat time-energy uncertainty relations
   http://arxiv.org/PS_cache/quant-ph/pdf/0304/0304206.pdf

Now apart from these mathematical principles, do you
or others know of examples in auditory *perception*
where training for certain classes of parameterized
(complex) sounds made the human hearing system
increasingly "beat" the frequency time uncertainty
relation in the above-described sense? If so, it
could prove highly relevant for the design of
"super-resolution" auditory displays. In fact in
my own application for the blind I already generate
more detail than one reasonably expects resolvable
under the uncertainty relation or under standard
spectrographic analysis, in part just because it does
no harm, but in part also because in principle the
listener could learn to exploit (even implicitly
acquired) a priori knowledge, and it would indeed be
extremely interesting if humans could adapt and learn
to exploit the underlying sound structure of what is
still left after passing the cochlea and early stages
of neural processing. Vice versa, one would then like
to know how one can help the human brain to do that.

Best regards,

Peter Meijer


Seeing with Sound - The vOICe
http://www.seeingwithsound.com
http://www.visualprosthesis.com


IEEE Spectrum, February 2004, pp. 13-14, "Sight for Sore Ears"
http://www.spectrum.ieee.org/WEBONLY/resource/feb04/0204neye.html