An apparatus for implementing a process for demodulating a carrier wave which is phase modulated by a subcarrier wave which is phase shift modulated by baseband signals, by which at least one phase demodulation process is performed using a Costas tracking loop to regenerate the carrier wave, wherein the baseband signals obtained are all subsequently sampled, then decoded, wherein a carrier wave frequency is first converted to an intermediate frequency which is lower than the carrier wave frequency, and the subcarrier wave is extracted by a phase demodulation process using a modified Costas loop, characterized by the fact that each "data" arm and "error" arm of the modified Costas loop comprises, in sequence, a demodulator mixer circuit which receives a waveform at subcarrier wave frequency, a bandpass filter, a sampling multiplier which receives a signal at a frequency which is twice the intermediate frequency, an analog to digital converter and a matched digital filter controlled by the bit clock frequency and the output of which is received by a multiplier of "data" and "error" arm signals.