From: email@example.com (Fred R. Goldstein)
Subject: Re: Hayes' New Modem
Date: 10 Jan 1994 05:41:34 GMT
Organization: Digital Equipment Corp., Littleton MA USA
In article <firstname.lastname@example.org> email@example.com (Jakob
> ...But there is an absolute limit (Shannon's Law). The
> question was about the transmission over a *real* phone line. And that
> means there exists *noise*. The limit of bps is proportional to the
> logarithm of the signal to noise ratio. Unfortunately I don't remember
> the constant factors.
Shannon's law is, in plaintext,
BPS(max) = Bw * log(2)((1+S)/N)
That is, take the signal-to-noise ration (adding 1 to signal, so a
negative SNR has some information present) and represent it as a power
of 2. Multiply by bandwidth (in Hz) and you get BPS.
THus if you have a 30 dB (1000) signal to noise ratio, that's 1001/1
which is a smidgen under 2^10. If you have 3000 Hz usable bandwidth
that's the 10 times 3000, or around 30000 bps max.
It was often said that a phone line couldn't go beyond 26000 bps or
so, based on the typical bandwidth and SNR. Today a good clean line
is more likely to be digitally switched at 64000 bps, which is well
above the Shannon limit (digitization is lossy), but you still get a
theoretical limit closer to 40 kbps. Thus V.34, at 28.8 kbps, is
pushing the envelope, but still possible. But it won't work on a line
that's transcoded down to 32 kbps, or just plain noisy. Note the 300
to 3400 Hz nominal frequency range; the 3400 is a hard filter.
Fred R. Goldstein k1io firstname.lastname@example.org
Opinions are mine alone; sharing requires permission