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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: Uncertainty principle debate*From*: Ramin Pichevar <Ramin.Pichevar@xxxxxxxxxxxxxx>*Date*: Fri, 30 Jan 2004 16:11:19 -0500*Delivery-date*: Fri Jan 30 16:42:26 2004*Importance*: Normal*In-reply-to*: <401AB256.3111@alum.mit.edu>*Reply-to*: Ramin Pichevar <Ramin.Pichevar@xxxxxxxxxxxxxx>*Sender*: AUDITORY Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

Fred, If I understand well your email, you mention that the uncertainty bound is not equal to 1/2 as derived by Gabor but much less than that (let say 0.004). But does this mean that there is no uncertainty? First of all, one should imagine an experiment in which he/she can find the difference between the two points you are talking about. In my opinion, the computation of this distance requires a threshold detecting device. Note that if we even imagine that an infinite precision threshold detectors exists, I am not sure that there won't be any time-frequency uncertainty in this device. In fact, a threshold detector is a device that compares values at times (t-n), (t-n+1), (t-n+2), ..., t in addition to comparing the current value at time t to a predefined threshold value (note that the slope is important to detect in-phase points and not out-of-phase (a lag equal to pi) points). If we accept this fact, then a very slow varying tone (with a very low frequency) will need a very long window (n) (the window used in the threshold detector). In my opinion, this implicitly implies the uncertainty somewhere. On the other hand, in quantum physics the bound is much smaller than 0.004 (in fact it is in the order of the Plank constant). In my opinion again, this means that theoritically we can develop other approaches (not in the framework of the Fourier transform but in another framework) that can give us much less uncertainty, but there will still be an uncertainty in our processings. Regards, Ramin -----Message d'origine----- De : AUDITORY Research in Auditory Perception [mailto:AUDITORY@LISTS.MCGILL.CA]De la part de herzfeld Envoye : 30 janvier, 2004 14:37 A : AUDITORY@LISTS.MCGILL.CA Objet : Uncertainty principle debate Hello List, The current controversy about the application of the uncertainty principl;e is to me at least interesting and somewhat perplexing in that it is still, seems to me, misunderstood. There are two two methods of defining frequency. One of these is the inverse of the time difference between two points of equal phase in a recurring signal. This definition is NOT limited by the uncertainty principle.[Kneser, H.O. Bermerkungen ueber Definition and Messung der Frequenz. Arch. Elekt. Uebertr. 1948 2 167-169} Bekesy in many of his works (based on experimental data) has stated : Frequency is already determined in 2 cycles of a sinusoidal signal. At a frequency of 500 Hz the estimate that I have is that the aproximate DL = 1 Hz. Now two cycles of 500 Hz is 4 mS. The product of delta t and delta f is 0.004. Very obviously less than 1/2 which (the 1/2) as I recall was first derived by Gabor [ Gabor, D. Theory of communication. J. Instn. Elect. Engrs. 1946 93(3) 429-457] See also [Licklider J.C.R. "Basic correlates of the auditory sto,i;is" in S.S. Stevens (ed) Handbook of experimental psychology pp 985-1013 1951 Wiley, New York] Licklider (one of my teachers) compares this to Heisenberg's uncertainty principle. Based on this type of data the determination of frequency by at least humans and perhaps other vertebrates must be based on time differences. Fred -- Fred Herzfeld, MIT'54 78 Glynn Marsh Drive #59 Brunswick, Ga. 31525-0504 USA Tel: (912) 262-1276 Fax: (912) 262-1276 by request

**References**:**Uncertainty principle debate***From:*herzfeld

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