The present invention relates to a technique for recovering each of an entire analog speech signal and a modulated data signal simultaneously received over a transmission channel such as a common analog telephone speech channel. In the received composite signal, the entire modulated data signal is multiplexed within the normal analog speech signal frequency band where the speech is present and its signal power density characteristic is at a low level. Separation of the speech and data signals at the receiver is effected by recovering the modulation carrier frequency and demodulating the received signal to recover the data signal. The data signal is then (a) remodulated with the recovered carrier, (b) modified to cancel phase jitter and frequency offset errors detected during the data demodulating process and (c) convolved with an arbitrary channel impulse response in an adaptive filter whose output signal is subtracted from the received composite data and speech signal to generate the recovered speech signal. To improve the recovered speech signal, a least mean square algorithm is used to update the arbitrary channel impulse response output signal of the adaptive filter.