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How the cochlea computes (2024)

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Re: How the cochlea computes (2024)

#61

Post by littlestymaar »

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?

A continuous sinusoidal sound, I guess?

Re: How the cochlea computes (2024)

#62

Post by kulahan »

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.

Re: How the cochlea computes (2024)

#63

Post by xeonmc »

JKCalhoun wrote: post #43
Chabsff wrote: post #16

Earlier quoted context omitted.

And phase. People always forget about the phase as if it was purely imaginary.

Ha ha, as I understand it, phase is imaginary in a Fourier transform. Complex numbers are used and the imaginary portion does indeed represent phase. I have been told that reversing the process — creating a time-based waveform — will not resemble (visually) the original due to this phase loss in the round-tripping. But then our brain never paid phase any mind so it will sound the same to our ears. (Yay, MP3!)

Actually, by the Kramers-Kronig relation you can infer the imaginary part just from the real parts, if given that your time signal is causal. So the phase isn’t actually lost in any way at all, if you assume causality.

Also, pedantic nit: phase would be the imaginary exponent of the spectrum rather than the imaginary part directly, i.e, you take the logarithm of the complex amplitude to get log-magnitude (real) plus phase (imag)

Re: How the cochlea computes (2024)

#64

Post by hansvm »

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?

It would look like a Fourier transform ;)

Zooming in to cartoonish levels might drive the point home a bit. Suppose you have sound waves

  |---------|---------|---------|
What is the frequency exactly 1/3 the way between the first two wave peaks? It's a nonsensical question. The frequency relates to the time delta between peaks, and looking locally at a sufficiently small region of time gives no information about that phenomenon.

Let's zoom out a bit. What's the frequency over a longer period of time, capturing a few peaks?

Well...if you know there is only one frequency then you can do some math to figure it out, but as soon as you might be describing a mix of frequencies you suddenly, again, potentially don't have enough information.

That lack of information manifests in a few ways. The exact math (Shannon's theorems?) suggests some things, but the language involved mismatches with human perception sufficiently that people get burned trying to apply it too directly. E.g., a bass beat with a bit of clock skew is very different from a bass beat as far as a careless decomposition is concerned, but it's likely not observable by a human listener.

Not being localized in time means* you look at longer horizons, considering more and more of those interactions. Instead of the beat of a 4/4 song meaning that the frequency changes at discrete intervals, it means that there's a larger, over-arching pattern capturing "the frequency distribution" of the entire song.

*Truly time-nonlocalized sound is of course impossible, so I'm giving some reasonable interpretation.

Re: How the cochlea computes (2024)

#65

Post by patrickthebold »

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…

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.

Re: How the cochlea computes (2024)

#66

Post by xeonmc »

patrickthebold wrote: post #65
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…

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.

You’ll also need to have existed and started listening before the beginning of time, forever and ever. Amen.

Re: How the cochlea computes (2024)

#67

Post by bragr »

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.

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

Re: How the cochlea computes (2024)

#68

Post by xeonmc »

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?

Means that it is a broad spectrum signal.

Imagine the dissonant sound of hitting a trashcan.

Now imagine the sound of pressing down all 88 keys on a piano simultaneously.

Do they sound similar in your head?

The localization is located at where the phase of all frequency components are aligned coherently construct into a pulse, while further down in time their phases are misaligned and cancel each other out.

Re: How the cochlea computes (2024)

#70

Post by cherryteastain »

patrickthebold wrote: post #65
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…

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.

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

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