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Re: human versus spectral resolution -- Gabor or Go Bare ?

Dick's and Alain's words of wisdom may need one point added.

Yes, because humans often seem to outperform a Heisenberg/Gabor theory-bound machine, it appears that we have two independent systems: one to analyze spectrum and one to analyze time, neither of them worrying much about what the other is doing. There are, however, some rules that the two systems must abide by, in order to do their job so exceedingly well: for frequency analysis to be accurate, the length of the time window must be precisely known (i.e., the start and the end of the observation interval); for time analysis the markers of the interval must be of identical (or nearly identical) spectral composition. In other words, to measure performance along one dimension, uncertainty along the other must be minimal.

I am grateful to Bill Hartmann for pointing my nose to ch. 13 of his "SSS" book, where he explains the uncertainty issue better than I have seen it done anywhere else (on my modest level of physics and mathematics). One thing, however, I want to point out is that studies in agreement with the delta-f--delta-t tradeoff, as far as I can tell, have used signals with dynamically changing spectra. That uncertainty of bandwidth was paired with the temporal uncertainty introduced by gradual onsets and/or offsets of the signal's temporal envelope (as Ronken [1971] did),  thus producing conditions ideal for testing the uncertainty theory's validity in psychoacoustics. The key word here is **dynamic** -- "bare" signals with firmly anchored temporal edges and spectra that stand steady for the duration of the observation interval are likely to produce results beating the theory's prediction.

Incidentally, a Gaborian tradeoff has been demonstrated between bandwidth and the angular resolution of **moving** sources (Chandler and Grantham [1992], JASA 91, 1624-36), as predicted by spatial extension of the uncertainty theory (Divenyi and Zakarauskas [1992], in Auditory physiology and perception, eds. Cazals, Demany & Horner, 563-70, Pergamon, London).


At 07:21 AM 4/4/2008, Michael Fulton wrote:
Just a quick thanks to anyone who replied to my earlier question(s)

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