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How the cochlea computes (2024)

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Re: How the cochlea computes (2024)

#101

Post by anyfoo »

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…

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 has a start and an end) and discrete. An FFT is effectively an implementation of a DFT, and there is nothing indicating to me that hearing is in any way specifically related to how the FFT computes a DFT.

But more importantly, I'm not sure DFT fits at all? This is an analog, real-world physical process, so where is it discrete, i.e. how does the ear capture samples?

I think, purely based upon its "mode", what's happening is more akin to a Fourier series, which is the missing fourth category completing (FT, DTFT, DFT): Continuous (non-discrete), but finite or rather periodic in time.

But secondly, unlike Gabor transforms, wavelet transforms are specifically not just windowed Fourier anythings (whether FT/FS/DFT/DTFT). Those would commonly be called "short-time Fourier transforms" (STFT, existing again in discrete and non-discrete variants), and the article straight up mentions that they don't fit either in its footnotes.

Wavelet transforms use an entirely different shape (e.g. a haar wavelet) that is shifted and stretched for analysis, instead of windowed sinusoids over a windowed signal.

And I think those distinctions are what the article actually wanted to touch upon.

Re: How the cochlea computes (2024)

#102

Post by aidenn0 »

BrenBarn wrote: post #53
xeonmc wrote: post #6

Nit: It’s an unfortunate confusion of naming conventions, but Fourier Transform in the strictest sense implies an infinite “sampling” period, while the finite “sample” period counterpart would correspond to Fourier Series even though we colloquially refer to them interchangeably. (I had put “sampling” in quotes as they’re actually “integration period” in this context of continuous time integration, though it would be…

Yeah, it's sort of like saying the ear doesn't do "a" Fourier transform, it does a bunch of Fourier transforms on samples of data, with a varying tradeoff between temporal and frequency resolution. But most people would still say that's doing a Fourier transform. As the article briefly mentions, it's a tempting hypothesis that there is a relationship between the acoustic properties of human speech and the physical/ne…

> ...it's a tempting hypothesis that there is a relationship between the acoustic properties of human speech and the physical/neural structure of the auditory system.

This seems trivially true in the sense that human speech is intelligible by humans; there are many sounds that humans cannot hear and/or distinguish, and speech does not involve those.

Re: How the cochlea computes (2024)

#104

Post by anyfoo »

IshKebab wrote: post #76
cherryteastain wrote: post #70

Earlier quoted context omitted.

Not really, just as we can create spectrograms [1] for a real time audio feed without having to wait for the end of the recording by binning the signal into timewise chunks. [1] https://en.wikipedia.org/wiki/Spectrogram

Those use the Short-Time Fourier Transform, which is very much like what the ear does. https://en.wikipedia.org/wiki/Short-time_Fourier_transform

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.

Re: How the cochlea computes (2024)

#106

Post by anyfoo »

superb-owl wrote: post #60

The title seems a little click-baity and basically wrong. Gabor transforms, wavelet transforms, etc are all generalizations of the fourier transform, which give you a spectrum analysis at each point in time The content is generally good but I'd argue that the ear is indeed doing very Fourier-y things.

Agree on the click-baity part, but as for being wrong... not if we're really pedantic. As you've said, Gabor and wavelet are basically generalizations of the Fourier Transform, not actually Fourier Transforms. Just like FS/DFT/DTFT aren't really Fourier Transforms either.

On one corner of the square, you have Fourier Transforms, which are essentially contiguous and infinite. On the opposite corner, you have the DFT, which is both finite (or periodic) and discrete. Hearing is more akin to a Fourier Series, which is finite/periodic but contiguous. That's probably not what the article aims at addressing, though.

But then wavelet transforms are different from Fourier Series again, because you have shifted and stretched shapes (some of them quite weird) instead of sinusoids.

But yeah, colloquially, I agree, the ear is indeed doing very Fourier-y things.

Re: How the cochlea computes (2024)

#107

Post by jibal »

SoftTalker wrote: post #33
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…

Ears evolved long before speech did. Probably in step with vocalizations however.

Ears arose long before speech did. They evolved in response to changes in the environment, e.g., the existence of speech.

Re: How the cochlea computes (2024)

#108

Post by fuzzfactor »

Terr_ wrote: post #96
bragr wrote: post #67

Earlier quoted context omitted.

Well without the humorous size difference, this is basically what whales and elephants do for long distance communication.

Was playing around with a fundamental frequency calculator [0] to associate certain sizes to hertz, then using a tone-generator [1] to get a subjective idea of what it'd sound like. Though of course, nature has plenty of other tricks, like how Koalas can go down to ~27hz. [2] [0] https://acousticalengineer.com/fundamental-frequency-calcula... [1] https://www.szynalski.com/tone-generator/ [2] https://www.nature.com/ar…

How long would a Dachshund have to be for it to sound like a 60 kilo Great Dane?

Re: How the cochlea computes (2024)

#109

Post by jibal »

kulahan wrote: post #62
shermantanktop wrote: post #38

The thesis about human speech occupying less crowded spectrum is well aligned with a book called "The Great Animal Orchestra" ( https://www.amazon.com/Great-Animal-Orchestra-Finding-Origin... ). That author details how the "dawn chorus" is composed of a vast number of species making noise, but who are able to pick out mating calls and other signals due to evolving their vocalizations into unique sonic niches. It's qu…

Probably worth mentioning that as evolutions that allow them to compete well in nature die out, ones that allow them to compete well in cities takes their place. Evolution is always a series of tradeoffs. Maybe we don't have sonic variation, but temporal instead.

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

Re: How the cochlea computes (2024)

#110

Post by IshKebab »

anyfoo wrote: post #104
IshKebab wrote: post #76

Earlier quoted context omitted.

Those use the Short-Time Fourier Transform, which is very much like what the ear does. https://en.wikipedia.org/wiki/Short-time_Fourier_transform

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".

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