[ILUG] Shannon's law (was : Genesis)

[Niall]

On Tue, 7 Mar 2000, Paul Jakma wrote:

>   For a phone line, however, to achieve Genesis' 45Mbit/s needs 
>   e.g. a bandwith of 2MHz and S/N of 70dB. The traditional bandwith of a
>   phone line is 3.1KHz (to allow frequencies from 300Hz to 3.4KHz)
> 
> but isn't there some law (corollary of shannon's law perhaps? or
> shannons law in reverse?) that states that to properly represent a
> given bitstream you must sample it at at least twice the rate of the
> bitstream? Eg Audio CD's are encoded at 44.1KHz because the human
> audible spectrum is 22KHz (for young uns anyway). So if that's
> correct then by your reckoning phone lines should have a bandwidth of
> at least 6.2KHz.

Nyquist's theorem tells us that to properly represent a signal BY SAMPLING
we must sample at twice the highest frequency in which we are interested.
However, an analog phone line doesn't use sampling - it's just passing an
analog signal.

> also, 6.2KHz seems a very poor figure for even the shittiest copper line

Yes, and 3.1KHz is even worse. Any phone line will have a much better
response than this (but won't however, approach the range of the young
un's ear from 20Hz to 22KHz). However, the 300Hz to 3.4KHz range was
chosen to make most conversation intelligible, yet to reduce the bandwith
as much as possible. This had nothing to do with local loop but everything
to do with long distance traffic where various forms of multiplexing are
used to put multiple conversations on one cable. When you do this, you
must arbitrarily choose how much of the conversation you encode, hence the
300Hz to 3.4KHz range mentioned.


Regards,

Niall  O Broin