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.
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:
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
Indeed this relates to a discussion that we had 9 years ago,
James D. (jj) Johnston
Independent Audio and Electroacoustics Consultant