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Re: Uncertainty principle debate
Nordmark (1968, 1970) made the same point. See also Moore (1973).
[Moore BCJ (1973) Frequency difference limens for short-duration
tones. J. Acoust. Soc. Am. 54:610-619; Nordmark JO (1968) Mechanisms
of frequency discrimination. J. Acoust. Soc. Am. 44:1533-1540;
Nordmark JO (1970) Time and frequency analysis. In Tobias JV (ed
Foundations of modern auditory theory. New York: Academic Press,
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
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 Herzfeld, MIT'54
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Brunswick, Ga. 31525-0504
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Fax: (912) 262-1276 by request
Alain de Cheveigne'
Ircam - CNRS,
1 place Igor Stravinsky, 75004, Paris, FRANCE.
email: Alain.de.Cheveigne@ircam.fr, phone: +33 1 44 78 48 46