From: goldstein@carafe.tay2.dec.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 <telecom14.19.10@eecs.nwu.edu> hummes@osf.org (Jakob Hummes) writes: > ...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 goldstein@carafe.tay2.dec.com Opinions are mine alone; sharing requires permission

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