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 they say the ear does a Fourier transform.

This article suggests it's accomplished by something between wavelet and Gabor. Which, yes, is not exactly a Fourier transform -- but it's producing something that is about 95-99% the same in the end.

And again, nobody would ever suggest the ear was performing the exact math that the FFT does, down to the last decimal point. But these filters still work essentially the same way as the FFT in terms of how they respond to a given frequency, it's really just how they're windowed.

So if anyone just wants a simple explanation, I would say yes the ear does a Fourier transform. A discrete one with windowing.

> 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 be about where exactly it is.

> but it does do a time-localized frequency-domain transform akin to wavelets

maybe easier to conceive of first as an arbitrarily defined filter bank based on physiological results rather than trying to jump directly to some neatly defined set of orthogonal basis functions. additionally, orthogonal basis functions cannot, by definition, capture things like masking effects.

> A more complicated hypothesis off the top of my head: the location of human speech in frequency/envelope is a tradeoff between (1) occupying an unfilled niche in sound space; (2) optimal information density taking brain processing speed into account; and (3) evolutionary constraints on physiology of sound production and hearing.

(4) size of the animal.

notably: some smaller creatures have supersonic vocalization and sensory capability, sometimes this is hypothesized to complement visual perception for avoiding predators, it also could just have a lot to do with the fact that, well, they have tiny articulators and tiny vocalizations!

> one would suspect that the specific characteristics of the human cochlea might be tuned to human speech while still being able to process environmental and animal sounds sufficiently well.

I wonder if these could be used to better master movies and television audio such that the dialogue is easier to hear.

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.

If you take this thought process even farther, specific words and phonemes should occupy specific slices of the tradeoff space. Across all languages and cultures, an immediate warning that a tiger is about to jump on you should sit in a different place than a mother comforting a baby (which, of course, it does.) Maybe that even filters down to ordinary conversational speech.

Analogy: when you knock on doors, how do you decide what rhythm and duration to use, so that it won’t be mistaken as accidentally hitting the door?

> 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?

Even if it is doing a wavelet transform, I still see that as made of Fourier transforms. Not sure if there's a good way to describe this.

We can make a short-time fourier transform or a wavelet transform in the same way either by:

- filterbank approach integrating signals in time

- take fourier transform of time slices, integrating in frequency

The same machinery just with different filters.

> A more complicated hypothesis off the top of my head: the location of human speech in frequency/envelope is a tradeoff between (1) occupying an unfilled niche in sound space; (2) optimal information density taking brain processing speed into account; and (3) evolutionary constraints on physiology of sound production and hearing.

Well from an evolutionary perspective, this would be unsurprising, considering any other forms of language would have been ill-fitted for purpose and died out. This is really just a flavor of the anthropic principle.

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

Is that an human understanding or is it just an AI that read the text and ignored the pictures?

Why do we need a summary in a post that adds nothing new to the conversation?

Do you believe it might be possible that the frequency band of human speech is not determined by such factors at all but more of a function of height? kids have higher voices adults have deeper voices. Similar to stringed instruments: viola high pitched and bass low pitched.

I'm no expert in these matters just speculating...

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.

It's a graduate student writing a journal club article about the Lewicki 2002 paper, which is very good, and whose abstract states the idea more precisely: "The form of the code depends on sound class, resembling a Fourier transformation when optimized for animal vocalizations and a wavelet transformation when optimized for non-biological environmental sounds"

Birds have also evolved to choose when to vocalize to best be heard - doing so earlier in urban areas where later there will be more traffic noise, and later in some forest environments to avoid being drowned out by the early rising noisy insects.

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.

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/neural structure of the auditory system. It's hard to get clear evidence on this but a lot of people have a hunch that there was some coevolution involved, with the ear's filter functions favoring the frequency ranges used by speech sounds.

I was a bit peeved by the title, but I think its a fair use of clickbait as the article has a lot of little details about acoustics in humans that I was unfamiliar with (i.e. a link to a primer on the the transduction implementation of cochlear cilia)

But yeah there is a strict vs colloquial collision here.

> analgous to the Pauli exclusion principle

Did you mean the Heisenberg Uncertainty Principle instead? Or is there actually some connection of Pauli Exlusion Principle to conjugate transforms that I was’t aware of?

> There is a trade off there between frequency and temporal precision

Sure, and the FFT isn't inherently biased towards one vs the other. If you take an FFT over a long time window (narrowband spectrogram) then you get good frequency resolution at the cost of time resolution, and vice versa for a short time window (wideband spectrogram).

For speech recognition ideally you'd want to use both since they are detecting different things. TFA is saying that this is in fact what our cochlea filter bank is doing, using different types of filter at different frequency ranges - better frequency resolution at lower frequencies where the formants are (carrying articulatory information), and better time resolution at the high frequencies generated by fricatives where frequency doesn't matter but accurate onset detection is useful for detecting plosives.

The ear clearly doesn't operate on "samples of data", it doesn't "take windowed samples" ... there's an ongoing mechanical process.

STFT?

It's a Copy>Paste Special>Transpose on a waveform, converting Rows/Columns that are time/amplitude (with wavelength embedded) into Rows/Columns that are frequency/amplitude (for a snapshot in time).

People love to go on about how brilliant it is and they're probably right but that's how I understand it.

3Blue1Brown has a really good explanation here: https://www.youtube.com/watch?v=spUNpyF58BY

It gave me a much better intuition than my math course.

Read this (which is free): The Scientist's and Engineer's Guide to Digital Signal Processing* https://www.dspguide.com

It's very comprehensive, but it's also very well written and walks you through the mechanics of Fourier transforms in a way that makes them intuitive.

It's an absolutely brilliant bit of maths that breaks a complex waveform into the individual components. Kind of like taking an orchestral song and then working out each individual instrument's contribution. Learning about this left me honestly aghast and in shock that it's not only possible but that someone (Joseph Fourier) figured it out and then shared it with the world.

This video does a great job explaining what it is and how it works to the layman. 3blue1brown - https://www.youtube.com/watch?v=spUNpyF58BY

Hahaha, I was working on learning these in second year uni… which was also exactly when I switched from an electrical engineering focussed degree to a software one!

Perhaps finally I should learn too…

the very simplest way to describe it: it is what turns a waveform (amplitude x time) to a spectrogram like on a stereo (amplitude x frequency)

humble plug https://dsego.github.io/demystifying-fourier/

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.

I find it beautiful to see the term "sinus wave."

No, it's vice versa. If two wind instruments play unison slightly out of tune from each other, it will be very noticeable. If the bass is slightly out of tune or mistakenly plays a different note a semitone up or down, it's easy to not notice it.

I haven't noticed that effect, to be honest. Actually I think its the really low bass frequencies that are harder to tune- especially if you remove the harmonics and just leave the fundamental.

Are you perhaps experiencing some high frequency hearing loss?

tinnitus

Would look still too much like wavelet.

Hopefully not ... it has been thoroughly debunked, whereas the theory of evolution is supported by massive amounts of data and is the foundation of the entire science of biology.

As low-level physical mechanistic processes? Absolutely not.

As higher-order, statistically transparent abstract nudges of providence existing outside the confines of causality? Metaphysically interesting but philosophically futile.

This is one of those pedant vs cocktail chatterer distinctions. It's an interesting dive and gives a nice, triggering, headline.

But, to the vast majority who don't really know or care about the math, "Fourier Transform" is, at best, a totem for the entire concept space of "frequency domain", "spectral decomposition", etc.

They are not making fine distinctions of tradeoffs among different methods. I'm not sure I'd even call it disinformation to tell this hand-wavy story and pique someone's interest in a topic they otherwise never thought about...

the closest i have been, was acoustic phase discrimination by owls.

there appears to be no software for this, its all hardware, the signal format flips as it travels through the anatomy.