Modem for telephone system

A modulator comprising a bit stream for converting a bit stream into a phase modulation symbol and a demodulator for converting the word phase symbol into a bit stream which is converted into a digital filtered signal which, when converted into an analog signal, And modulates the modulation signal from the phase modulation symbol value by a predetermined frequency. The analog signal is mixed with a predetermined frequency steady-state signal to provide a phase-phase intermediate frequency signal which is recovered from the received digital signal by a means including a microprocessor. The word demodulator operates in a training mode in which a string of predetermined symbols is sent to the modulator and the resulting modulating signal is sent to the demodulator, and the stored filter coefficients of the microprocessor word coincide with the predetermined symbol in the modulator The