The 56k modem speed is actually a theoretical number arising from the
64K available (in theory) to every phone conversation encoded to digital
form and then back to analog.

To save on the cost of having an extra clock wire for certian portions
of the digital transmission, the last bit of each byte is toggled,
regardless of the actual value of that bit from the A/D conversion.
This enables easy clock recovery for the phone company, and one less
dedicated wire for the clocking circuit.

8 bits at 8kHz is 64kbps on the standard pots line.  7 bits at 8khz is -
tada, 56kbps.

Further, this data rate is only from the phone company to the end user,
the upload speed is at 33.6kbs or less.  The modems used are actually
connected to the digital side of the circuit, rather than on the other
end of a set of a/d and d/a converters.  The modems do some rather
impressive wire and a/d-d/a characterization in the beginning with
various noises to figure out how much of the system they can overcome,
but to really get the data at the full rate they'd have to up the power
levels a bit from the phone company's side.

As far as the other rates below 56k, they were simply what engineers
could reliably attain given a technology, cost limit, and corporate
politics of each time.  In each case except 56k they dictated the wire
speed, and any gains on compression were above that.

Of course, the 56k calculation and bit about the phone companies
throwing away the last bit for clocking purposes is out of a DSP book.
The rest is either rampant speculation on my part, or things I've read
that I now assume I deduced myself.  Read accordingly...

-Adam

James Newton, Host wrote:

>Why is each higher baud rate twice as fast until 14.4K which is only 1.5
>times faster than 9600?
>
>115,200
> 57,600
> 28,800
> 14,400
>    ?
>  9,600
>  4,800
>  2,400
>  1,200
>    600
>    300
>
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