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The bandwidth of human hearing by empirical data is $20 \; Hz$ to $20 \; kHz$. A cochlear implant stimulates the auditory or acoustic or Cochlear nerve directly so that the hearing can be improved in the case of stimulation mechanism upstream of the Cochlear nerve has degraded.

Let us assume that the ear mechanism has not degraded (such as in a young and healthy adult). The Cochlear implant can likely improve hearing, even in this case, by increasing the bandwidth by amplifying the effect of the ear drum vibration (sensor actuation). However the neurons connecting the Cochlear nerve to the hearing region of the brain have an upper limit on the sampling rate on the order of $1 \; kHz$.

Does the the Nyquist sampling theorem limit the superhuman hearing and sound localization capability made possible by a Cochlear implant?

https://en.wikipedia.org/wiki/Hearing_range#/media/File:Animal_hearing_frequency_range.svg

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    $\begingroup$ I think it's just the physiology that gets in the way: there simply aren't sensors and neurons specialized for those frequencies (i.e. there is no internal clock). $\endgroup$ – a concerned citizen Apr 8 at 7:13
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    $\begingroup$ This is better asked on biology.SE. A greater cochlear frequency wouldn't necessarily imply the rest of involved components can actually process the signal for hearing, I'd imagine. $\endgroup$ – OverLordGoldDragon Apr 8 at 8:16
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    $\begingroup$ The number of neurons allocated is dynamic. Blinded kids may reallocate visual neurons to learn better audio echo location than sighted adults. $\endgroup$ – hotpaw2 Apr 8 at 9:59
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    $\begingroup$ BTW, that's a very interesting plot, I didn't know the hearing range of so many species was known. I wonder, though, why does a cow need that dynamic range?? $\endgroup$ – MBaz Apr 8 at 13:30
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    $\begingroup$ @wizzwizz4 - evolution is not purposeful in a sense of their being an active agent directing it, but it's not random either. Natural selection does quite a good job at steering evolution towards a better adapted forms of life. $\endgroup$ – Davor Apr 8 at 14:42
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Does the Nyquist frequency of the Cochlear nerve impose the fundamental limit on human hearing?

No.

A quick run-through the human auditory system:

  1. The outer ear (pinnae, ear canal), spatially "encodes" the sound direction of incidence and funnel the sound pressure towards the
  2. ear drum, which converts sound into physical motions, i.e. mechanical energy
  3. The middle ear (ossicles) is a mechanical transformer (with some protective limiting built-in) that impedance matches the air-loaded ear drum to the liquid-loaded oval window of the
  4. Cochlea (inner ear). The vibration excites a bending wave on the basilar membrane. The membrane is highly resonant and transcodes frequency into location: for any given frequency the location of the resonance peak is in a different spot. High frequencies wiggle very close to the oval window, low frequencies towards the end of it. This motion is picked up by the
  5. Cochlea neurons, which transmit the intensity of the excitation at their location to the brain. About 20% of the neurons are efferent (come out of the brain) and are used to actively tune the resonance with a feedback loop (which causes tinnitus if misadjusted)

So in essence the Basilar Membrane performs sort of a mechanical Fourier transform. The frequency selectivity of the Neurons is NOT determined by the firing pattern but simply by their location. A neuron at the beginning of the basilar membrane is sensitive to high frequencies and a neuron at the end detects low frequencies. But they are more or less the same type of Neurons.

The Nyquist criteria doesn't come into play at all since no neuron is trying to pick up the original time domain waveform. The couldn't anyway: human neurons have a maximum firing rate of less than 1000 Hz and average firing rates are way below that. The firing rate of a cochlea neuron represents "Intensity at a certain frequency" where that frequency is determine by the location of that specific neuron.

So you can think of it as a short term Fourier Transform. Instead of a single time domain signal you get a parallel stream of frequency domain signals where each individual signal has a much lower bandwidth.

A cochlea implant basically does the short term Fourier transform internally and then connects the output for each frequency range to the "matching" neurons in the cochlea nerve. Theoretically you can create ">20 kHz" hearing with an implant that can actually receive and process higher frequencies and simply routes them to existing neurons, i.e. you could feed 40 kHz activity to the 10 kHz Neuron. The human would have a sensation when exposed to 40 kHz but it's unclear what they could do with that: they would have "relearn" how to hear. Aside from the highly questionable practical and ethical issues, it probably wouldn't be useful. In order to get to 40 kHz you'd have to give some other frequencies, and chances are that evolution has chosen the current "normal" range for humans pretty carefully.

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    $\begingroup$ "you could feed 40 kHz activity to the 10 kHz Neuron" isn't this how cochlear implants work in some cases? If a person can only hear in a narrow range of frequencies, then they can get an implant or hearing aid that down shifts the sound into that range? $\endgroup$ – eipi Apr 8 at 16:38
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    $\begingroup$ Depends. Cochlea implants are most valuable if the cochlea itself or the cilia (hair cells) are damaged but the cochlea nerve is still mostly intact. In this case you would route the frequency bands to those nerve endings that are the most "natural" fit. If there is also damage to the cochlea nerve, you can indeed try to reroute the most important frequency bands (speech intelligibility) to whatever nerve endings are still functional. That tricky though. $\endgroup$ – Hilmar Apr 8 at 17:03
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    $\begingroup$ I'm always so amazed at how many parts there are to the auditory system, my best friend is a Speech Language Pathologist and we've talked about this before. Just a two way conversation between two people, like hearing someone talk and saying something back has so many parts to it, and so many ways for it to go wrong. We all take it for granted. it's such a fascinating crossover between biology and engineering. I would have loved to go into it as a dsp engineer. $\endgroup$ – eipi Apr 8 at 19:09
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    $\begingroup$ @kb314 "The 10 kHz neuron" meaning the one that's triggered by the hair that responds to 10 kHz sounds. You could run your own Fourier transform and trigger that neuron for 40 kHz sounds instead. $\endgroup$ – Tavian Barnes Apr 8 at 19:50
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    $\begingroup$ @kb314: the firing rate of the neuron is NOT related to the frequency itself. It's related to the intensity at that frequency band. It's like the cone cells in your eye: the S-cell does not try to follow the actual light waveform (which is a whopping 714 Tera Hz) but it encodes the intensity at that frequency. The firing rate of neuron is typically in the 10s to 100s per second for strong simulation regardless of frequency $\endgroup$ – Hilmar Apr 8 at 19:59
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The auditory system encodes sound in frequency domain, i.e. the activation levels of auditory nerve fibers represent the amplitude or energy in a frequency band assigned to that particular fiber. The ear itself does the transformation from time to frequency domain.

If you somehow modified the ear itself to be sensitive to higher frequencies, the output axons would have no problem handling that, because the frequency information is encoded in the selection of the axon, not in its firing rate. Modifying a functional ear is generally frowned upon, but if the ear is non-functional, it's all bets off. E.g. a cochlear implant can give you decent echolocation abilities if it has wider input bandwidth and maps this wider frequency range to the existing axons. With a suitable (even purely mechanical) clicker that produces short acoustic pulses, you can "see" with your ears. Humans have some rudimentary echolocation ability even without such aids - it requires practice to be able to use it, of course. Widening the ear's functional bandwidth improves the spatial resolution.

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