Data rates in PSTNs:

A voice channel in a PSTN is band limited with a nominal bandwidth of 3.1 kHz. A first-cut estimate of this can be attained from Nyquist's theorem that applies to noiseless channels and states:

 R = 2H log V bps

 Where

 R = maximum data rate H = bandwidth of the channel V = number of discrete levels in the signal

For a 3-kHz channel and a binary signal, maximum data rate works out to be 600 bps, if channel is ideal. In a practical channel, maximum rate would come down. By increasing number of levels used to signify the signal, bit rate can be increased arbitrarily in a noiseless channel. It is significant to recognize that actual number of signal transitions is still limited to binary level limit; effective bit rate goes up with more than twosignal levels as each signal level can nowsignify a group of two or more bits. Maximum rate of signal transitions which can be supported by a channel is called symbol rate or baud rate. In a channel where noise is present, there is an absolute maximum limit for the bit rate. This limit arises as the difference between two signal levels becomes comparable to the noise level when number of signal level is increased. Claude Shannon extended Nyquist's work to case of noisy channels affected by thermal or random noise. Shannon's result defines;

R = H log (1+S/N)

 Where R= the maximum bit rate obtainable

H= bandwidth of the channel

S/N = signal to noise ratio.