digital audio for mice

[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.

Is this a contradiction?




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]

So what will be your advice for the mouse?

[Nordic]

[el`Ol]

The mouse isn´t amused.

[Aud1073cH]

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.