Re: 57600 modems

Marc Lindahl (
Wed, 27 Nov 1996 13:06:27 -0500

Hoo, boy! You need to check your math, man!

Here's a web page which describes briefly USR's 56K tech:

FYI, standard phone line bandwidth is 4KHz; and using engineering rule of
thumb, given a 3000Hz bandwidth, the highest representable 'well defined'
square wave would be 300Hz. Using a simple coding method like NRZI, that
would yield 300 bps. Further, sending data over wire is best thought of in
terms of Shannon's information theory. If we have a 4Hkz bandwidth, we can
transmit 8K baud, or symbols. This is due to Nyquist's theory (we're
sampling the channel at 8KHz -- just like a CD player with a 22.05 KHz
bandwidth is sampled at 44.1KHz.) Since phone A/D's and D/A's are 8 bits,
each baud can (in a practical sense) represent up to 8 bits, max. So we
are sending 8 bits at an 8KHz rate, we get 64Kbps. This is the information
capacity of the channel. The 56K comes from the practical: the phone
system uses 'robbed bit signalling' where they steal some bits for ring
indication, etc. It's really not necessary to understand the actually
modulation algorithms, etc. since we can easily calculate the upper bound
of the channel capacity, which is the bottom line anyway! Additionally,
note that 4KHz was chosen by the telco as being a reasonable minimum
bandwidth for clearly understanding speech.

At 10:27 AM +0500 11/27/96, Jesus Maria Arango - Ing. Comunicaciones FSM
LTDA. wrote:
>This sound very interesting but I have a little theorical objection to
>this point of view.
>Telephone lines have a bandwith of 3000 Hz. while human voice has a
>bandwith of 18000 Hz. Our voice does not sound the same over the phone
>because an 18000Hz signal has to be fit into 3000Hz.
>Now, when speaking of digital signals (Square signals) there is a theory
>that says that any square signal can be generated by a sum of several sine
>and cosine signals of diferent frequency. The more bandwidth you have the
>more sine and cosine signals you can add and thus the square signal will
>be better. Also, the more speed you need, you will also need more sine and
>cosine waves, so you will need more bandwidth. This is why people
>mistakenly asociate bandwith with speed. This theory comes from Furier's
>series, which can be use to find that if we have a phone line with 3000 Hz
>then the maximum speed of a well defined square signal will be 9600 bps.
>How do we get 28800? Easy, computer signal are not transmited in square
>form, they are converted (modulated) into an analog representation which
>supports greater speed.
>Now, knowing that it is not efficient to transmit data over the phone in
>square form. I don't understand how can someone fit 56700 into a phone
>line in square form.

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