# digital audio for mice

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#### el`Ol

Hello all!

Assume there is a mouse that wants high quality digital audio. Its hearing range is from 500Hz to 120Khz, two octaves less than humans. Its neurons and receptor cells don´t switch faster, and it has much less of them. But every expert the mouse asked told it that it needs six times the amount of audio data than humans to be satisfied.

Oliver

#### Speedskater

If the only frequency that humans could hear was 20 KHz and the only frequency that mice could hear was 120 KHz. Then the mouse would need 6 times the "digital" data. It's all about sample rate.

#### el`Ol

If both only heard these frequencies, the amount of data would be the same, because one would only have to encode the phase and amplitude information fast enough for the neurons.

#### I_Forgot

What does "six times the amount of audio data" mean? That is a hand-waving, smoke-and-mirrors, totally meaningless term if I ever heard one. Sounds like something that someone in an audio marketing dept would say, not someone steeped in the scientific method. Are you reading hifi marketing literature for some sort of tweeter?

I_F

#### el`Ol

The mouse isn´t amused.

#### Aud1073cH

a scientific approach?

Here's my attempt at the scientific approach.

So how much data do humans need to hear up to 20kHz, and how much would said mouse need at 120kHz? Is it six times?

For this argument it will be given that the audio will be stored in a PCM format. Also, the bit depth will remain at a constant 16 bits. When scaling, one byte shall be eight bits. One kilobyte (kB) shall be 1,024bytes. One megabyte (MB) shall be 1,024kilobytes.

The Nyquist-Shannon sampling theorem states:

If a function f(t) contains no frequencies higher than W cps, it is completely determined by giving its ordinates at a series of points spaced 1/(2W) seconds apart.

In short, the highest frequency which can be accurately represented is less than one-half of the sampling rate. So for this argument, the sampling frequency will be twice the audio frequency.

For humans hearing at 20kHz, we will need a sample rate of 40kHz. (*I know CDs are 44.1kHz, this is just for this argument.)
so 16bits*40,000samples/sec =704,000bits/sec
multiplying by 60seconds/min = 42,240,000bits/min = 5,280,000bytes/min = 5156.25kB/min = 5.035400390625MB/min

or roughly 5MB/min (per channel of audio) -10MB/min stereo

The mouse hearing at 120kHz, we will need a sample rate of 240kHz.
so 16bits*120,000samples/sec =3,840,000bits/sec
multiplying by 60seconds/min = 230,400,000bits/min = 28,800,000bytes/min = 28,125kB/min = 27.4658203125MB/min

or roughly 27.5MB/min (per channel of audio) -55Meg/min stereo

So we would need about 5.5 (about six, the original estimate) times more data for the same length of audio at 120kHz than we do at 20kHz. QED quod erat demonstrandum

I don't know what the difference would be if we went to a direct stream digital (DSD) pulse-density modulation, one bit audio solution. Standard DSD (SA-CD) at a 1bit sample depth with 2.8224MHz sample rate (64x oversampling 44.1kHz) takes the same amount of data as a standard PCM CD, and claims a frequency responce of 100kHz with that rate. This mouse would need to move up to 128 or 256 times oversampling, but I don't know the frequency response gained with those rates.

#### Speedskater

Typo error:
so 16bits*120,000samples/sec =3,840,000bits/sec
Should be:
so 16bits*240,000samples/sec =3,840,000bits/sec

Math error:
so 16bits*40,000samples/sec =704,000bits/sec
Should be:
so 16bits*40,000samples/sec =640,000bits/sec

I'll leave the conclusion correction to the OP.

#### neutron7

actually mice only live about 2 years, so mice years are about 1 / 40th of human years

that means mice seconds are also shorter. and 120khz is only 3 Kmicehertz.

you mean kMHz

#### I_Forgot

Let's say you had a gun with a laser sight. No, I mean let's say the sight is a laser that can burn things. Now let's say the gun shoots depleted uranium bullets at maybe 4000 ft/sec. Now let's say the laser is infrared and is powered by a nuclear generator. Let's say it's small enough to fit into a standard sized backpack. If you shoot at the moon with that gun, will the laser or the bullet do more damage to a car that gets in the way? Oh oh! Let's say the car has a turbo charger! Now will the bullet do more damage or will the laser? What if you increased the power of the nuclear generator to 15 Gigawatts? Now let's say an airplane is flying by at 400 mph. If the bullet hits the plane will it crash or just explode in the air? If the laser hits the plane will it cut in half and fall in two pieces or will it explode in the air?

I_F

#### Nordic

Hey if you are shooting depleted uranium, you may as well use the newly unveiled HERCULES lazer with it.... (The name is in caps)

said laser contains 300 terawatts of power (or 300 times the capacity of the entire US electricity grid) and could "help scientists develop better proton and electron beams for radiation treatment of cancer."

"If you could hold a giant magnifying glass in space and focus all the sunlight shining toward Earth onto one grain of sand, that concentrated ray would approach the intensity of "HERCULES"

#### el`Ol

I_Forgot said:
Let's say you had a gun with a laser sight. No, I mean let's say the sight is a laser that can burn things. Now let's say the gun shoots depleted uranium bullets at maybe 4000 ft/sec. Now let's say the laser is infrared and is powered by a nuclear generator. Let's say it's small enough to fit into a standard sized backpack. If you shoot at the moon with that gun, will the laser or the bullet do more damage to a car that gets in the way? Oh oh! Let's say the car has a turbo charger! Now will the bullet do more damage or will the laser? What if you increased the power of the nuclear generator to 15 Gigawatts? Now let's say an airplane is flying by at 400 mph. If the bullet hits the plane will it crash or just explode in the air? If the laser hits the plane will it cut in half and fall in two pieces or will it explode in the air?

I_F

If I understand you right you refer to applying a certain amount of energy in a more or less focused way. To make my initial post even more precise: Time resolution of neural systems can be higher than that of single neurons, but that requires large neuron assemblies, so the mouse should have a disadvantage even there, despite its capabilities of detecting higher frequencies. So no better focusing.

#### gtforme00

Perhaps the limitation of human hearing is not in the switching "speed" of the neurons and receptor cells, but in the mechanical limitations of the ossicular chain. As I understand it, the ossicles are tuned by small muscles to create what amounts to physiological acoustic filters. It seems reasonable that the ossicles of mice, having smaller physical dimensions, would have higher natural frequencies than those of humans.

Regards,
David

#### tINY

Someone who was really cleaver might be able to use under/oversampling (aka aliasing) to capture 0.5 - 120kHz in less than 240kS/s.

But the processing would make it tough. And it migh have significant distortions...

I think you really need to determine mouse Psycho-acoustics and develop a codec based on that. We could call it MouseDisk or DCCm....

Of course, the audiophile mice will still want their little vinyl disks.

-tINY

#### el`Ol

Time to come to the point (that is not about mice):

In PCM and bitstream-coding you need half the amount of data for the top octave, what is in strong contrast to its importance. And in good PCM you even need an octave more, only to get the filter artefacts out of the audible spectrum. In good bitstream coding you need two octaves to keep the noise out of the audible spectrum.
Correct me if I´m wrong, but as far as I know, in lossy fourier-based coding the situation isn´t much different. Wavelet analysis devides the signal in octaves, so maybe it is a better starting point.

Any ideas for an implementation?

#### tINY

I haven't kept up lately:

There were some people looking at wavelet encoding for video and maybe phone audio (which is very bandwidth sensitive).

For high quality audio, memory and computing power are enough now that there really isn't a need to get too fancy. 24/96 and lossless compression (like .zip technology) are really the way to go.

-tINY

#### kvk

Use MP3 and you'll get 67,000 songs on a chip the size of the dot at the end of this sentence. They'll sound crappy to both human and rodent but who cares because the original recordings never vary in volume by more than +- .0003dB so they'll both get tired of listening in three or four minutes anyway and go eat Cheeze-Its.

#### jlsem

and go eat Cheeze-Its

That wasn't necessary. A lot of sensible people, like myself, enjoy Cheeze-Its.

John

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