Join the discussion
Write your take first — we'll ask for email only when you're ready to publish.
- Hacker News
- As the auditory associative cortex in parietal lobe discriminates frequencies, there must be some time-frequency transform between the ear and the brain. This must be discrete (as neurons fire in bursts and there is a finite frequency resolution capacity) and finite time.
The poor man's conversion of finite to equivalent infinite time is if you assume an infinite signal where the initial finite one is repeated infinately to the past and the future.
by tsoukase - 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.
by javier_e06 - man I need to finally learn what a Fourier transform isby tryauuum
- humble plug https://dsego.github.io/demystifying-fourier/by dsego
- 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)by adzm
- 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…
by jama211 - 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
by garbageman - 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.
by anigbrowl - 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.
by CGMthrowaway - 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.
by TobTobXX - Just a warning that the video ends with a loud, high pitched tone that will make you want to rip your headphones off.
Ironic for a video about hearing.
by Cadwhisker - 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.by adornKey
- 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.by empiricus
- I find it beautiful to see the term "sinus wave."by FarmerPotato
- 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.by kragen
- Nice to see a video for the tip links and ion channels.
I spent a while reading up on that stuff because I was trying to figure what causes my tinnitus. My best guess is if the hairs over bend, that stuff can break and an ion channel get stuck open causing the cell to fire continually.
Another fun ear fact is they incorporate active amplification. You can hook an electrical signal to the loudspeaker type cell to make it vibrate around https://youtu.be/pij8a8aNpWQ
by tim333 - Wow, this discussion about how our ears work is mind-blowing! It's amazing how complex sound processing is, and the comparison to signal processing concepts is really illuminating.by rattan12138
- 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.
- 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.
by dsp_person - > 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?
by lgas - 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?by xeonmc
- > 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.
by km3r - 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.
- > 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!
by a-dub - 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.
by crazygringo - 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)
by xeonmc - 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.
by BrenBarn - 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.
by meowkit - > 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.
by kazinator