As the sensitivity of the human ear is from 20 Hz to 20 kHz?

Question

As the sensitivity of the human ear is from 20 Hz to 20 kHz why sound on audio cds & high definition discs are sampled at 44.1 kHz,48 kHz,96 kHz & 192 kHz ?

Answer 1

Because they are digital conversions of analog signals.

Nyquist Therom says that you need to sample at least twice the frequency of your highest frequency to be able to accurately reproduce the signal. Still, you can increase your sampling rate, and it will only improve the signal quality.

When you digitize the audio, and then reconvert it back to analog your going to lose part of the signal, by increasing the sampling rate your able to better replicate the signal.

Just because your ear can only hear up to 20kHz, doesn't really have any correlation to the sampling rate. When the speaker converts the electrical signals back into sound, it's going to need to have a high sample rate, or else it will sound like crap.

Answer 2

Because sampling has to do with how often the music is looked at by the digital hardware, not with what the human ear can hear. In fact, recommended sampling is at least twice what is wanted in the playback, so 44.1 is about the minimum for including 20 kHz.
Since human speech (not singing) is usually a much narrower range, it is possible to sample radio talk shows and recorded speeches such as Congress at a lower rate, such as 22 kHz without losing understandibility while saving storage space.

Answer 3

One reason is "real life" hardware. (specifically "anti-alias filters")

As people have said, Nyquist theorem says you need sample rates that are double the bandwidth of the signal in order to be able to fully reconstruct the signal. Hence, one may think, 40kHz would do nicely.

However, this assumes there are no sounds above 20kHz being recorded. Anything above 20kHz gets "wrapped around", so a recorded 21kHz sound would come out of your CD player as a 19kHz sound (which you can hear), a 30kHz recorded sound would come out as a 10kHz signal and so on.

Hence you need to filter (in analog, i.e. before sampling). That stops sounds above your "maximum" frequency from being recorded. This is called an "anti-alias" filter.

Real-life filters don't have instant cut-off (i.e. you can't have 20kHz unaffected and 20.00001kHz completely removed), so you need to add a little bit of leeway. This means that if the maximum frequency you want recorded accurately is 20kHz, then sounds up to, say, 22kHz will still be audible, just quieter.

If you want cheaper hardware, you can sample more quickly and allow yourself a less effective filter, hence some of the higher sampling rates. In fact you can then use digital filters (i.e. inside a computer) to cut down this bandwidth to fit inside 44.1kHz, or you could not bother and sell it as a "96kHz sample-rate CD" for twice as much money.

OK, that last bit was a bit cynical :) One big advantage for audio CDs with the much higher sample rates is you can use a much more "gentle" filter... the less leeway you give your filter, the more distortion you'll add to the signal below 20kHz.

Answer 4

Shannons theory states that to sample a wave correctly you need at least double the rate of the highest frequency. This is the minimum and you will get small improvements with faster rates. However 192 seems over the top to me.