Subject: Re: Uncertainty principle debate From: Peter Meijer <peter.b.l.meijer(at)PHILIPS.COM> Date: Wed, 11 Feb 2004 17:25:35 +0100Hi 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