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How the cochlea computes (2024)

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Re: How the cochlea computes (2024)

#131

Post by kragen »

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.

I think those bursts ("action potentials") happen at continuously varying times, though.

Re: How the cochlea computes (2024)

#132

Post by kragen »

waffletower wrote: post #123
crazygringo wrote: post #88

Earlier quoted context omitted.

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 f…

Many solutions to differential equations are thoroughly derived from the Fourier transform too, and so is Heisenberg's uncertainty principle. That doesn't mean they're the same thing.

Re: How the cochlea computes (2024)

#133

Post by kragen »

bonoboTP wrote: post #71
patrickthebold wrote: post #65

Earlier quoted context omitted.

I think I might be missing something basic, but if you actually wanted to do a Fourier transform on the sound hitting your ear, wouldn't you need to wait your entire lifetime to compute it? It seems pretty clear that's not what is happening, since you can actually hear things as they happen.

Yes, for the vanilla Fourier transform you have to integrate from negative to positive infinity. But more practically you can put put a temporally finite-support window function on it, so you only analyze a part of it. Whenever you see a 2d spectrogram image in audio editing software, where the audio engineer can suppress a certain range of frequencies in a certain time period they use something like this. It's calle…

Yeah. But a really annoying thing about the STFT is that its temporal resolution is independent of frequency, so you either have to have shitty temporal resolution at high frequencies or shitty frequency resolution at low ones, compared to the human ear. So in Audacity I keep having to switch back and forth between window sizes.

Re: How the cochlea computes (2024)

#134

Post by kragen »

IshKebab wrote: post #110
anyfoo wrote: post #104

Earlier quoted context omitted.

Yes, but the article specifically says that it isn't like a short-time fourier transform either, but more like a wavelet transform, which is different yet again.

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".

It's very unlike both of those, as the nice diagrams in the article explain; not only is what it is saying not obvious to you, it is apparently something you actively disbelieve.

Re: How the cochlea computes (2024)

#135

Post by kragen »

lgas wrote: post #59
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…

> It does this because the sounds processed by the ear are often localized in time. What would it mean for a sound to not be localized in time?

The 50-cycle hum of the transformer outside your house. Tinnitus. The ≈15kHz horizontal scanning frequency whine of a CRT TV you used to be able to hear when you were a kid.

Of course, none of these are completely nonlocalized in time. Sooner or later there will be a blackout and the transformer will go silent. But it's a lot less localized than the chirp of a bird.

Re: How the cochlea computes (2024)

#136

Post by taneq »

Terr_ wrote: post #57
a-dub wrote: post #30

Earlier quoted context omitted.

> At high frequencies, frequency resolution is sacrificed for temporal resolution, and vice versa at low frequencies. this is the time-frequency uncertainty principle. intuitively it can be understood by thinking about wavelength. the more stretched out the waveform is in time, the more of it you need to see in order to have a good representation of its frequency, but the more of it you see, the less precise you can…

> it also could just have a lot to do with the fact that, well, they have tiny articulators and tiny vocalizations! Now I'm imagining some alien shrew with vocal-cords (or syrinx, or whatever) that runs the entire length of its body, just so that it can emit lower-frequency noises for some reason.

I’m not sure exactly how, but cats can emit a surprisingly low growl when they want to. Like, as deep as a large human would be able to. So there’s more going on than just linear size… And how I’m wondering what the lowest recorded pitch made by a shrew is.

Re: How the cochlea computes (2024)

#138

Post by kragen »

adornKey wrote: post #35

This subject has bothered me for a long time. My question to guys into acoustics was always: If the cochlea performs some kind of Fourier transform, what are the chances, that it uses sinus waves as a base for the vector-space? - if it did anything like that it could just as good use any slightly different wave-forms as a base for transformation. Stiffness and non-linearity will for sure take care that any ideal rubb…

Oh, it turns out that complex exponentials are the eigenfunctions of linear time-invariant systems, and sound transmission is full of linear time-invariant systems. So surely ears cannot be perfectly detecting sinusoids, but there's a lot of evolutionary pressure to come as close as possible. That way, you can still recognize a birdsong or the howl of a wolf even if it echoes off a cliff, or recognize your baby crying even if it is facing the other way.

Re: How the cochlea computes (2024)

#139

Post by kragen »

adornKey wrote: post #89
empiricus wrote: post #83

Earlier quoted context omitted.

well, cochlea is working withing the realm of biological and physical possibilities. basically it is a triangle through which waves are propagating, and sensors along the edge. smth smth this is similar to a filter bank of gabor filters that respond to rising freq along the triangle edge. ergo you can say fourier, but it only means sensors responding to different freq becasue of their location.

Yeah, but not only the frequency is important - the wave-form is very relevant. For example if your wave-form is a triangle, listerners will tell you that it is very noisy compared to a simple sinus. If you use sinus as a base of your vector space triangles really look like a noisy mix. My question is, if the basic elements are really sinus, or if the basic Eigen-Waves of the cochlea are other Wave-Forms (e.g. slight…

But if you apply a frequency-dependent phase shift to the triangle wave, nobody will be able to tell the difference unless the frequency is very low.

Re: How the cochlea computes (2024)

#140

Post by didroe »

kulahan wrote: post #120
jibal wrote: post #109

Earlier quoted context omitted.

The dying out of birds "in nature" and the adaptations to cities are largely independent as they occur in different populations.

It's about filling open niches. City birds were an open niche for a long time. The ones who adapted to handle that better are thriving in better population numbers than those which can only survive with 13 specific types of trees. Even still, among the populations of birds not adapting to the city, they are being forcibly adapted in other ways. If the reach is too big, they die. This is how evolution works, and has a…

The problem is that evolution works on a much longer timescale than the pace of change to the environment that humans cause.
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