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

[Kenn Humborg]

On Tue, Mar 07, 2000 at 12:19:21AM +0000, Paul Jakma wrote:
> 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.

To properly represent an _analogue_ signal with discrete samples,
you must sample at at least twice the highest frequency in the signal.

Completely different to what you said.

I guess a corollary is that you can represent a bit stream of speed
N bits per second as an analogue signal with max frequency component
N/2 Hz.

> also, 6.2KHz seems a very poor figure for even the shittiest copper
> line, doesn't it?

It's not really the line itself (although shitty _long_ lines are a 
contributor).  It's the circuitry at each end of the line.  Remember that
the 'protocol' (i.e. electrical interface) at that phone socket on your
wall goes back about 70 years.  Specifications like 'how to tell a ring
signal' and 'how to signal off-hook' are remarkably primitive.

There are also filters at various points to limit the signal to the 300
to 3400Hz band.  Nasty, evil, 12-pole filters...

Later,
Kenn

PS.  Funny that we're talking about phones.  My phone was dead
     when I came home this evening.  Called in a fault report and
     now it's working again.  Pretty good considering the rep said
     no one would be available until Wednesday morning :-)