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Re: Human hearing beats the Fourier uncertainty principle: Research
I haven't fully read the article, but a quick comment would be that the accuracy ofÂfrequency estimation of a single tone is not limited by the uncertainty principle, human or machine alike. It is limited by Cramer-Rao lower bound and I remember the mean square error of an optimal frequencyÂestimatorÂis proportional to SNR/(time)^3, if the noise is additive white Gaussian noise.
The uncertainty principle still governs the resolution of between time and frequency **when multiple tones are present**. If two concurrent tones are separated by delta_f, then it requires at least longer than 1/delta_f to resolve the tones in the spectrum.Â
I'd be moreÂinterested to see if human pitch detection can violate the Cramer-Rao bound.
Such is my two pennies,
On Saturday, February 16, 2013, Kevin Austin wrote:
>> (Phys.org)âFor 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 performance.
>> Read more at: http://phys.org/news/2013-02-human-fourier-uncertainty-principle.html#jCp
Yi-Wen Liu ååæ, Ph.D.
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