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Re: Human hearing beats the Fourier uncertainty principle: Research

A million years ago (it seems), I investigated the acoustical uncertainty principle for my PhD thesis. I found that humans did a pretty good job at optimally resolving narrow-band short-duration noise stimuli, and did best for stimuli with a bandwidth-duration product of around 2. By optimally, I mean compared to an ideal observer theory. There was no indication my observers were able to beat the uncertainty principle, but they came close to operating as well as an ideal observer for some bandwidth-duration conditions.


Any study showing observers “beating” the uncertainty principle has subjects who are solving the task differently to what the experimenter expected, or there are issues with defining bandwidth and duration. IMHO.






From: AUDITORY - Research in Auditory Perception [mailto:AUDITORY@xxxxxxxxxxxxxxx] On Behalf Of corey
Sent: Friday, 22 February 2013 05:33
To: AUDITORY@xxxxxxxxxxxxxxx
Subject: Re: Human hearing beats the Fourier uncertainty principle: Research


I do think this article is misleading.  In my opinion the uncertainty principle is not something to be "overcome".  It simply relates the bandwidth of a waveform to its duration (which is an unassailable fact).  In Fourier theory frequency is defined for periodic signals (which are of infinite duration).  Any finite duration signal can be viewed equally as an infinite duration periodic signal that has been multiplied by a finite duration window.  It is this windowing process that introduces a spread of frequencies (after all the window is a waveform too).  It is thus not physically possible to create stimuli that "beat" the uncertainty principle, which seems to negate the conclusions in the remainder of the article.


On 2013-02-20, at 10:27 AM, James Johnston wrote:

Well, yes. Of course, and the FFT is not a minimum-phase filter, while the ear is very close to such. Well, there goes a large speed factor already, eh?

On Wed, Feb 20, 2013 at 8:48 AM, Bastian Epp <bepp@xxxxxxxxxxxxxx> wrote:

Hi list!

without having read the paper in detail, I just think the discussion should be done with fair weapons:

The description of the ear via a FFT is a rather poor model, but a FFT (or rather the math behind that) can be interpretet as a bank of overlapping bandpass filters (see the Oppenheim Schaefer DSP book)....so this point raised is not valid.

I would be surprised if this result would not have been reported before in the solid psychoacoustics literature before.



On 02/18/2013 05:00 PM, James Johnston wrote:

I must admit some frustration with this particular paper. First, the
Gabor limit does not apply to the task, and never did. The only limit
here is SNR_based, since there is already expectation of a given set
of frequencies, this is not a task requiring arbitrary detection.
Then, the fact that the ear is a leading edge detector has been
understood for roughly 100 years now, making "1/100 th of a
wavelength" perhaps not such a big deal.
It is nice that this performance ability by the human has been clearly
demonstrated, but the headline is inexcusably misleading, and is
already providing fodder for the audiophile "I told you so" bunch who
simply doesn't understand what it means.
And, in any case, who would use an FFT to detect such a thing? Rather
use a set of bandpass filters, eh?
On Sun, Feb 17, 2013 at 12:02 PM, Peter Meijer
<feedback@xxxxxxxxxxxxxxxxxxx> wrote:
Indeed this relates to a discussion that we had 9 years ago,
and that formed the basis of my old web page on beating the
frequency-time uncertainty principle,
Best regards,
Peter Meijer
Seeing with Sound - The vOICe
Date: Sun, 17 Feb 2013 07:43:35 +0000
From: "Beerends, J.G. (John)" <john.beerends@xxxxxx>
To: AUDITORY@xxxxxxxxxxxxxxx
Subject: Re: Human hearing beats the Fourier uncertainty principle:
For discrimination the uncertainty limit does not exist, one can build
discriminator devices that go below the uncertainty limit in both the time
and frequency domain, the uncertainty limit is only a measure for the spread
(Delta) in both domains (DfDt>1), it is not a limit to what extent they can
be discriminated. One can also build a device that measures the frequency of
a sine wave with an accuracy below the uncertainty limit by exploiting
a-priori knowledge, i.e. if I know  that the signal I am measuring is a
short cut out of an infinite duration sine wave of a certain amplitude I can
measure the frequency as accurate as I want.
John Beerends
-----Original Message-----
From: AUDITORY - Research in Auditory Perception
[mailto:AUDITORY@xxxxxxxxxxxxxxx] On Behalf Of Kevin Austin
Sent: Saturday, February 16, 2013 5:07 PM
To: AUDITORY@xxxxxxxxxxxxxxx
Subject: Human hearing beats the Fourier uncertainty principle: Research
(Phys.org)-For the first time, physicists have found that humans can
discriminate a sound's frequency (related to a note's pitch) and timing
(whether a note comes before or after another note) more than 10 times
better than the limit imposed by the Fourier uncertainty principle. Not
surprisingly, some of the subjects with the best listening precision were
musicians, but even non-musicians could exceed the uncertainty limit. The
results rule out the majority of auditory processing brain algorithms that
have been proposed, since only a few models can match this impressive human
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Bastian Epp

Assistant Professor


DTU Electrical Engineering


Technical University of Denmark


Department of Electrical Engineering

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James D. (jj) Johnston

Independent Audio and Electroacoustics Consultant