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Human hearing beats FFT
ncdrawl
post Feb 9 2013, 15:20
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http://phys.org/news/2013-02-human-fourier...-principle.html
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2Bdecided
post Feb 11 2013, 19:02
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By taking an FFT, you are performing an (approximate, with issues) time/frequency analysis. You can picture is as a time/frequency grid. Click on "spectral view" in your favourite audio editor, and there it is (but only the amplitude is visible; FFT phase is vital too).

If you use a short FFT, you have fine time resolution, but wide frequency bins.
If you use a longer FFT, you have fine frequency resolution, but longer time bins.

e.g. sampling at 44.1kHz:
a 64-point FFT gives you blocks 1.5ms apart, and 689Hz apart.
a 1024-point FFT gives you blocks 23ms apart, and 43Hz apart.
a 65536-point FFT gives you blocks 1.5 seconds apart, and 0.7Hz apart.

The analysis limit claimed for FFT in that paper (and derived right at the start), is 4*pi better than just hitting the nearest block in this spectral grid would give you.

The human auditory system is doing 10x better than this.

The human auditory system is stunningly good at picking out the start of sharp-onset notes - it amplifies the onset greatly.
IIRC the human auditory system doesn't use the (fairly poor) frequency resolution of its filterbank to determine pitch. There are a couple of different models of how pitch perception probably works, but counting cycles and/or tracking harmonics are the simplest (not entirely accurate) ones. They barely need the filter bank at all.

I'm hoping someone will explain this better though.

Cheers,
David.
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Posts in this topic
- ncdrawl   Human hearing beats FFT   Feb 9 2013, 15:20
- - probedb   QUOTE (ncdrawl @ Feb 9 2013, 14:20) http:...   Feb 9 2013, 15:51
|- - ncdrawl   QUOTE (probedb @ Feb 9 2013, 09:51) QUOTE...   Feb 9 2013, 16:02
|- - probedb   QUOTE (ncdrawl @ Feb 9 2013, 15:02) it is...   Feb 11 2013, 09:26
- - lvqcl   From the comments: QUOTE The Fourier uncertainty ...   Feb 9 2013, 16:10
- - greynol   That title? What about the title of this discussi...   Feb 9 2013, 18:00
- - Alexey Lukin   Love the title   Feb 9 2013, 20:13
- - greynol   ...with a blunt stick.   Feb 9 2013, 20:17
- - Woodinville   Ad the Gabor limit does not address known frequenc...   Feb 10 2013, 04:41
|- - Kees de Visser   QUOTE (Woodinville @ Feb 10 2013, 04:41) ...   Feb 10 2013, 08:31
|- - Woodinville   QUOTE (Kees de Visser @ Feb 9 2013, 23:31...   Feb 10 2013, 12:51
|- - Porcus   QUOTE (Kees de Visser @ Feb 10 2013, 08:3...   Feb 10 2013, 17:15
- - 2Bdecided   Is it worth spending $25 to read this in full...   Feb 11 2013, 10:25
|- - Kees de Visser   I just stumbled upon this blog. Are we heading tow...   Feb 11 2013, 10:56
||- - Porcus   QUOTE More pointedly: until scientists devise and ...   Feb 11 2013, 11:46
||- - 2Bdecided   QUOTE (Porcus @ Feb 11 2013, 10:46) QUOTE...   Feb 11 2013, 12:21
|- - ojdo   QUOTE (2Bdecided @ Feb 11 2013, 17:25) Is...   Feb 11 2013, 17:13
- - db1989   Given that the writer misspelled mathematical and ...   Feb 11 2013, 16:39
|- - Ethan Winer   QUOTE (db1989 @ Feb 11 2013, 10:39) Given...   Feb 11 2013, 23:05
- - greynol   Would someone mind correlating the article with th...   Feb 11 2013, 16:48
- - benski   Off the top of my head. I might be wrong. But pa...   Feb 11 2013, 18:32
- - 2Bdecided   By taking an FFT, you are performing an (approxima...   Feb 11 2013, 19:02
- - krabapple   Here's what the audiophilosphere reliably take...   Feb 12 2013, 07:18
- - knutinh   Is not some wavelet/filterbank transform more rele...   Feb 12 2013, 09:59
|- - Garf   QUOTE (knutinh @ Feb 12 2013, 09:59) Is n...   Feb 19 2013, 17:27
|- - jmvalin   QUOTE (Garf @ Feb 19 2013, 11:27) Yes, th...   Feb 19 2013, 21:07
- - scuttle   I thought it would be fun and informative to poke ...   Feb 17 2013, 17:33
- - Willakan   Good God, I have been reading/getting PMed on othe...   Feb 18 2013, 20:03
|- - Porcus   QUOTE (Willakan @ Feb 18 2013, 20:03) or ...   Feb 18 2013, 20:22
|- - Woodinville   QUOTE (Willakan @ Feb 18 2013, 11:03) Goo...   Feb 19 2013, 00:44
- - 2Bdecided   It's amazing what people conclude, given that ...   Feb 19 2013, 10:53
- - lvqcl   I didn't find any mention of FFT in this artic...   Feb 19 2013, 15:51
|- - greynol   QUOTE (lvqcl @ Feb 19 2013, 06:51) I didn...   Feb 19 2013, 16:56
- - Canar   The first thing that comes to my mind is: Now how ...   Feb 19 2013, 16:46
|- - Garf   QUOTE (Canar @ Feb 19 2013, 16:46) The fi...   Feb 19 2013, 17:32
- - Paulhoff   For those in the know.......... The Princess an...   Feb 20 2013, 19:51
- - Woodinville   It's still a confused headline. Recognzing one...   Feb 21 2013, 04:55
|- - Garf   QUOTE (Woodinville @ Feb 21 2013, 04:55) ...   Feb 21 2013, 07:54
|- - Woodinville   QUOTE (Garf @ Feb 20 2013, 22:54) QUOTE (...   Feb 22 2013, 04:22
- - dhromed   Yeah, we don't want to turn HA into an extensi...   Feb 21 2013, 10:02
- - 2Bdecided   Never mind the title, I still don't find a sat...   Feb 25 2013, 13:14
|- - knutinh   QUOTE (2Bdecided @ Feb 25 2013, 13:14) Ne...   Feb 25 2013, 15:32
||- - 2Bdecided   QUOTE (knutinh @ Feb 25 2013, 14:32) I gu...   Feb 25 2013, 17:24
|- - jmvalin   QUOTE (2Bdecided @ Feb 25 2013, 07:14) Ne...   Feb 26 2013, 00:10
- - Woodinville   There are a number of issues confused in this thre...   Feb 26 2013, 04:30
|- - Alexey Lukin   QUOTE (Woodinville @ Feb 25 2013, 23:30) ...   Mar 14 2013, 17:39
- - 2Bdecided   Thank you JJ.   Feb 26 2013, 10:57
- - krabapple   http://arstechnica.com/science/2013/02/hum...3s-so...   Feb 27 2013, 01:51
- - greynol   Well the quality of the comments look pretty encou...   Feb 27 2013, 02:44
|- - Woodinville   QUOTE (greynol @ Feb 26 2013, 17:44) Well...   Feb 27 2013, 05:55
- - 2Bdecided   Interesting paper, thank you.   Mar 15 2013, 12:15
- - Yaakov Gringeler   EST is a new transform that can explain the result...   Apr 2 2013, 01:03
|- - Woodinville   QUOTE (Yaakov Gringeler @ Apr 1 2013, 17...   Apr 2 2013, 23:47
|- - Yaakov Gringeler   EST stands for Exponential Sum Transform and it us...   Apr 3 2013, 01:42
|- - Porcus   I think I could very well use a formula or two ......   Apr 3 2013, 20:34
- - Alexey Lukin   Yaakov, also check out the Reassigned spectrogram ...   Apr 2 2013, 23:59
- - Canar   I think a lot of us here would be interested in a ...   Apr 3 2013, 05:27
|- - Yaakov Gringeler   QUOTE (Canar @ Apr 3 2013, 05:27) I think...   Apr 3 2013, 18:14
- - db1989   If I may guess, I think he means that this site ha...   Apr 3 2013, 18:31
- - Yaakov Gringeler   The following link: http://www.mediafire.com/view...   Apr 3 2013, 22:10
- - Woodinville   Hm. Define "noiseless". Most instrumen...   Apr 11 2013, 11:09
- - Yaakov Gringeler   The paper described the mathematical basis of EST,...   Apr 11 2013, 19:33
|- - Woodinville   QUOTE (Yaakov Gringeler @ Apr 11 2013, 11...   Apr 11 2013, 20:36
|- - Yaakov Gringeler   QUOTE (Woodinville @ Apr 11 2013, 20:36) ...   Apr 11 2013, 21:32
|- - Woodinville   QUOTE (Yaakov Gringeler @ Apr 11 2013, 13...   Jun 4 2013, 01:51
- - Specy   Over 10 years ago, for my master thesis, I wrote a...   Aug 17 2013, 11:52
- - Yaakov Gringeler   Several months ago, in posts in this topic, I prov...   Nov 4 2013, 20:15


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