Subject: Re: Human hearing beats the Fourier uncertainty principle: Research From: Yi-Wen Liu <jacobliu@xxxxxxxx> Date: Sun, 17 Feb 2013 15:22:16 +0800 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>--485b397dd77bd1a36604d5e67766 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Hi there, I haven't fully read the article, but a quick comment would be that the accuracy of frequency 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 frequency estimator is 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. I'd be more interested to see if human pitch detection can violate the Cramer-Rao bound. Such is my two pennies, Yi-Wen On Saturday, February 16, 2013, Kevin Austin wrote: > Comments? > > > >> http://phys.org/news/2013-02-human-fourier-uncertainty-principle.html > >> > >> > >> (Phys.org)=E2=80=94For the first time, physicists have found that huma= ns 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 tha= t > have been proposed, since only a few models can match this impressive hum= an > performance. > >> > >> Read more at: > http://phys.org/news/2013-02-human-fourier-uncertainty-principle.html#jCp > > > Thanks > > Kevin --=20 Yi-Wen Liu =E5=8A=89=E5=A5=95=E6=B1=B6, Ph.D. http://www.ee.nthu.edu.tw/ywliu/ "Silver and gold have I none; but such as I have give I thee." --485b397dd77bd1a36604d5e67766 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Hi there,=C2=A0<div><br></div><div>I haven't fully read the article, bu= t a quick comment would be that the accuracy of=C2=A0frequency estimation o= f a single tone is not limited by the uncertainty principle, human or machi= ne alike. It is limited by Cramer-Rao lower bound and I remember the mean s= quare error of an optimal frequency=C2=A0estimator=C2=A0is proportional to = SNR/(time)^3, if the noise is additive white Gaussian noise.</div> <div><br></div><div>The uncertainty principle still governs the resolution = of between time and frequency **when multiple tones are present**. If two c= oncurrent tones are separated by delta_f, then it requires at least longer = than 1/delta_f to resolve the tones in the spectrum.=C2=A0</div> <div><br></div><div>I'd be more=C2=A0<span></span>interested to see if = human pitch detection can violate the Cramer-Rao bound.</div><div><br></div= ><div>Such is my two pennies,</div><div><br></div><div>Yi-Wen</div><div><br= > On Saturday, February 16, 2013, Kevin Austin wrote:<br><blockquote class= =3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padd= ing-left:1ex">Comments?<br> <br> <br> >> <a href=3D"http://phys.org/news/2013-02-human-fourier-uncertainty-= principle.html" target=3D"_blank">http://phys.org/news/2013-02-human-fourie= r-uncertainty-principle.html</a><br> >><br> >><br> >> (Phys.org)=E2=80=94For the first time, physicists have found that = humans can discriminate a sound's frequency (related to a note's pi= tch) and timing (whether a note comes before or after another note) more th= an 10 times better than the limit imposed by the Fourier uncertainty princi= ple. Not surprisingly, some of the subjects with the best listening precisi= on were musicians, but even non-musicians could exceed the uncertainty limi= t. The results rule out the majority of auditory processing brain algorithm= s that have been proposed, since only a few models can match this impressiv= e human performance.<br> >><br> >> Read more at: <a href=3D"http://phys.org/news/2013-02-human-fourie= r-uncertainty-principle.html#jCp" target=3D"_blank">http://phys.org/news/20= 13-02-human-fourier-uncertainty-principle.html#jCp</a><br> <br> <br> Thanks<br> <br> Kevin</blockquote></div><br><br>-- <br>Yi-Wen Liu =E5=8A=89=E5=A5=95=E6=B1= =B6, Ph.D.<br><a href=3D"http://www.ee.nthu.edu.tw/ywliu/" target=3D"_blank= ">http://www.ee.nthu.edu.tw/ywliu/</a><br>"Silver and gold have I none= ; but such as I have give I thee."<br> --485b397dd77bd1a36604d5e67766--