Modem for telephone system

A modem including a modulator section for converting a bit stream, wherein each given number of successive bits defines a symbol, into a phase modulated intermediate frequency (IF) signal, the symbols in the modulator section being phase modulated and then digitally filtered to provide a filtered signal that, when converted into an analog signal, provides a modulation signal of a frequency that is centered about a predetermined frequency and deviates therefrom in accordance with the value of the phase modulated symbol, the analog signal then being filtered and passed to a mixer for up conversion to an IF signal; and a demodulator section for converting the IF signal into a bit stream, the demodulator section including a microprocessor which not only filters received digital signals but contains a memory for storing filter coefficients for use in the filtering of received digital signals; the modem being also operable in a training mode wherein a sequence of predetermined symbols is provided to the filter in the modulator section and the resultant phase modulated IF signal is receivable in the demodulator section, the microprocessor acting to adjust the filter coefficients stored in its memory until the reconstructed phase modulated symbols correspond to the sequence of predetermined symbols provided to the filter in the modulator section.