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How the cochlea computes (2024)

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Re: How the cochlea computes (2024)

#121

Post by a-dub »

anyfoo wrote: post #117
actionfromafar wrote: post #114

Earlier quoted context omitted.

Don’t neurons fire in bursts? That’s sort of discrete I guess.

Even if they do (and I honestly have no idea), isn't it the frequency , i.e. the output of the basilar membrane in the ear, and not a sample in time of the actual sound wave which would correspond to a short-time frequency transform, that gets sampled here? And the basilar membrane seems like a pretty un-discrete (in time, not in frequency) process to me. But I'm not 100% sure. Sure, if you go small enough, you end u…

going all the way out to percept, the response of the system is non-linear: https://en.wikipedia.org/wiki/Mel_scale

this is believed to come from the shape of the cochlea, which is often modeled as a filterbank that can express this non-linearity in an intuitive way.

Re: How the cochlea computes (2024)

#123

Post by waffletower »

crazygringo wrote: post #88
edbaskerville wrote: post #21

To summarize: the ear does not do a Fourier transform, but it does do a time-localized frequency-domain transform akin to wavelets (specifically, intermediate between wavelet and Gabor transforms). It does this because the sounds processed by the ear are often localized in time. The article also describes a theory that human speech evolved to occupy an unoccupied space in frequency vs. envelope duration space. It mak…

Yeah, this article feels like it's very much setting up a ridiculous strawman. Nobody who knows anything about signal processing has ever suggested that the ear performs a Fourier transform across infinite time . But the ear does perform something very much akin to the FFT (fast Fourier transform), turning discrete samples into intensities at frequencies -- which is, of course, what any reasonable person means when t…

The article does a fair job of positing that the ear provides temporal/frequency resolution along a logarithmic scale but doesn't assert clearly that this resolution is fixed with the STFT and the Gabor variant. It hints that wavelets are more akin in terms of perceptual scaling as a function of frequency but not articulately. But it is interesting that the author's thesis, how Fourier mathematics isn't appropriate for describing human perception of sound, relates human hearing to the Gabor transform which is thoroughly a derivative of discrete Fourier mathematics.

Re: How the cochlea computes (2024)

#125

Post by shannifin »

I've always thought the basilar membrane was a fascinating piece of biological engineering. Whether or not the difference between its behavior vs FT really matters depends on the context. Audio processing on a computer, FFT is often great. Trying to understand / model human sound perception, particularly in relation to time, FFT has weaknesses.

Re: How the cochlea computes (2024)

#126

Post by [deleted] »

xeonmc wrote: post #32
bobmcnamara wrote: post #24

Earlier quoted context omitted.

But mostly not for ears it turns out! Phase matters for some wideband signals, but most folks struggle to tell apart audio from hilbert-90-degree-shifted-audio

Phase is required if it is to be a reversible transform. Otherwise would just be a Functional.

[deleted]

Re: How the cochlea computes (2024)

#127

Post by jibal »

anyfoo wrote: post #112
IshKebab wrote: post #110

Earlier quoted context omitted.

Barely different though. Obviously nobody is saying it's exactly a Fourier transform or a STFT. But it's very like a STFT (or a wavelet transform). The article is pretty much "cows aren't actually spheres guys".

I'd say the title is like that (and I agree with someone else's assessment of it being clickbait-y). I think the actual article does a pretty good job in distinguishing a lot of these transforms, and honing into which one matches most. But the title instead makes it sound (pun unintended) that what the ear does is not about frequency decomposition at all.

The fourth sentence in the article is "Vibrations travel through the fluid to the basilar membrane, which remarkably performs frequency separation", with the footnote

"We call this tonotopic organization, which is a mapping from frequency to space. This type of organization also exists in the cortex for other senses in addition to audition, such as retinotopy for vision and somatotopy for touch."

So the cochlea does frequency decomposition but not by performing a FT (https://en.wikipedia.org/wiki/Fourier_transform), but rather by a biomechanical process involving numerous sensors that are sensitive to different frequency ranges ... similar to how we have different kinds (only 3, or in birds and rare humans 4) of cones in the retina that are sensitive to different frequency ranges.

The claim that the title makes it sound like what the ear does is not about frequency decomposition at all is simply false ... that's not what it says, at all.

Re: How the cochlea computes (2024)

#128

Post by acjohnson55 »

actionfromafar wrote: post #114
anyfoo wrote: post #101

Earlier quoted context omitted.

Since we're being pedantic, there is some confusion of ideas here (even though you do make a valid overall point), and the strawman may not be as ridiculous. First, I think when you say FFT, you mean DFT. A Fourier transform is both non-discrete and infinite in time. A DTFT (discrete time fourier transform) is discrete, i.e. using samples, but infinite. A DFT (discrete fourier transform) is both finite (analyzed data…

Don’t neurons fire in bursts? That’s sort of discrete I guess.

Yes. See the volley theory of hearing: https://en.wikipedia.org/wiki/Volley_theory

Re: How the cochlea computes (2024)

#129

Post by ddingus »

antognini wrote: post #73

If you want to get really deep into this, Richard Lyon has spent decades developing the CARFAC model of human hearing: Cascade of Asymmetric Resonators with Fast-Acting Compression. As far as I know it's the most accurate digital model of human hearing. He has a PDF of his book about human hearing on his website: https://dicklyon.com/hmh/Lyon_Hearing_book_01jan2018_smaller...

Thank you! This is an excellent work. Much appreciated

Re: How the cochlea computes (2024)

#130

Post by kragen »

crazygringo wrote: post #88
edbaskerville wrote: post #21

To summarize: the ear does not do a Fourier transform, but it does do a time-localized frequency-domain transform akin to wavelets (specifically, intermediate between wavelet and Gabor transforms). It does this because the sounds processed by the ear are often localized in time. The article also describes a theory that human speech evolved to occupy an unoccupied space in frequency vs. envelope duration space. It mak…

Yeah, this article feels like it's very much setting up a ridiculous strawman. Nobody who knows anything about signal processing has ever suggested that the ear performs a Fourier transform across infinite time . But the ear does perform something very much akin to the FFT (fast Fourier transform), turning discrete samples into intensities at frequencies -- which is, of course, what any reasonable person means when t…

> turning discrete samples into intensities at frequencies

This description applies equally well to the discrete wavelet, discrete Gabor, and maybe even Hadamard transforms, which are definitely not, as you assert, "95–99% the same in the end" (how would you even measure such similarity?) So it is not something any reasonable person has ever meant by "the Fourier transform" or even "the discrete Fourier transform".

Also, you seem to be confused about what "discrete" means in the context of the Fourier transform. The ear functions in continuous time and does not take discrete samples.

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