The ear does not do a Fourier transform
93 comments
·October 30, 2025edbaskerville
crazygringo
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.
a-dub
> 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!
Terr_
> 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.
Y_Y
Sounds like an antenna, if you'll accept electromagnetic noise then there are some fish that could pass for your shrew, e.g. https://en.wikipedia.org/wiki/Gymnotus
bragr
Well without the humorous size difference, this is basically what whales and elephants do for long distance communication.
km3r
> 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.
kiicia
You are expecting too much, we still have no technology to do that, unless it’s about clarity of advertisement jingles /s
patrickthebold
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.
bonoboTP
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 called the short-time Fourier transform (STFT).
xeonmc
You’ll also need to have existed and started listening before the beginning of time, forever and ever. Amen.
cherryteastain
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.
IshKebab
Those use the Short-Time Fourier Transform, which is very much like what the ear does.
IshKebab
Yes exactly. This is a classic "no cats and dogs don't actually rain from the sky" article.
Nobody who knows literally anything about signal processing thought the ear was doing a Fourier transform. Is it doing some like a STFT? Obviously yes and this article doesn't go against that.
matthewdgreen
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.
xeonmc
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?
lgas
> 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?
hansvm
It would look like a Fourier transform ;)
Zooming in to cartoonish levels might drive the point home a bit. Suppose you have sound waves
|---------|---------|---------|
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.
jancsika
> It's a nonsensical question.
Are you talking about a discrete signal or a continuous signal?
xeonmc
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.
littlestymaar
A continuous sinusoidal sound, I guess?
dsp_person
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.
antognini
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...
shermantanktop
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 quite interesting but also a bit depressing as he documents the decline in intensity of this phenomenon with habitat destruction etc.
HarHarVeryFunny
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.
superb-owl
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.
kazinator
> A Fourier transform has no explicit temporal precision, and resembles something closer to the waveforms on the right; this is not what the filters in the cochlea look like.
Perhaps the ear does someting more vaguely analogous to a discrete Fourier transforms on samples of data, which is what we do in a lot of signal processing.
In signal processing, we take windowed samples, and do discrete transforms on these. These do give us some temporal precision.
There is a trade off there between frequency and temporal precision, analgous to the Pauli exclusion principle in quantum mechanics. The better we know a frequency, the less precisely we know the timing. Only an infinite, periodic signal has a single precise frequency (or precise set of harmonics) which are infinitely narrow blips in the frequency domain.
The continuous Fourier transform deals with periodic signals only. We transform an entire function like sin(x) over the entire domain. If that domain is interpreted as time, we are including all of eternity, so to speak from negative infinite time to positive.
xeonmc
> 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?
kvakkefly
They are not connected afaik.
HarHarVeryFunny
> 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.
energy123
STFT?
xeonmc
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 less immediately evocative of the concept people are colloquially familiar with. If we actually further impose a constraint of finite temporal resolution so that it is honest-to-god “sampling” then it becomes Discrete Fourier Transform, of which the Fast Fourier Transform is one implementation of.)
It is this strict definition that the article title is rebuking, but it’s not quite what the colloquial usage loosely evokes in most people’s minds when we usually say Fourier Transform as an analysis tool.
So this article should have been comparing to Fourier Series analysis rather than Fourier Transform in the pedantic sense, albeit that’ll be a bit less provocative.
Regardless, it doesn’t at all take away from the salient points of this excellent article which are really interesting reframing of the concepts: what the ear does mechanistically is applying a temporal “weigting function” (filter) so it’s somewhere between Fourier series and Fourier transform. This article hits the nail on the head on presenting the sliding scale of conjugate domain trade offs (think: Heisenberg)
BrenBarn
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.
foobarian
This is something you quickly learn when you read the theory in the textbook, get excited, and sit down to write some code and figure out that you'll have to pick a finite buffer size. :-)
meowkit
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.
fennec-posix
"It appears that human speech occupies a distinct time-frequency space. Some speculate that speech evolved to fill a time-frequency space that wasn’t yet occupied by other existing sounds."
I found this quite interesting, as I have noticed that I can detect voices in high-noise environments. E.g. HF Radio where noise is almost a constant if you don't use a digital mode.
amelius
What does the continuous tingling of a hair cell sound like to the subject?
rolph
supplemental:
Neuroanatomy, Auditory Pathway
https://www.ncbi.nlm.nih.gov/books/NBK532311/
Cochlear nerve and central auditory pathways
https://www.britannica.com/science/ear/Cochlear-nerve-and-ce...
Molecular Aspects of the Development and Function of Auditory Neurons
javier_e06
This is fascinating.
I know of vocoders in the military hardware that encode voices to resemble something more simple for compression (a low-tone male voice), smaller packets that take less bandwidth. This evolution of the ear to must also have evolved with our vocal chords and mouth to occupy available frequencies for transmission and reception for optimal communication.
The parallels with waveforms don't end there. Waveforms are also optimized for different terrains (urban, jungle).
Are languages organic waveforms optimized to ethnicity and terrain?
Cool article indeed.
null
adornKey
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 rubber model in physics will in reality be different from the perfect sinus.
empiricus
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.
adornKey
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. slightly wider or narrower than sinus, ...). If physics in the ear isn't linear, maybe sinus isn't the purest wave-form for a listener.
Most people in Physics only know sinus and maybe sometimes rectangles as a base for transformations, but mathematically you could use a lot of other things - maybe very similar to sinus, but different.
FarmerPotato
I find it beautiful to see the term "sinus wave."
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 makes no explicit connection between that fact and the type of transform the ear does—but 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.
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.