The problem of communication would have been trivial if the channel through which the signal must propagate were ideal, that is, an all pass system with a linear phase response. In practice, channels are non-ideal;​ imperfections in the physical channel, such as time-dispersion and frequency-dispersion, are the results of signal dependent distortions. In addition, upon reception the signal is further corrupted by the inevitable presence of additive random noise. Time dispersion causes successive pulses to overlap, thereby creating a phenomenon which has been termed 'intersymbol interference'. Frequency dispersion causes the received signal spectrum to vary both in amplitude and phase. Unless these channel imperfections are taken into account in the design of the communication system, the rate of data transmission can be limited by the physical channel. Also, the presence of additive noise poses further limitations on the ultimate performance of the system.

This thesis is concerned with adaptive signal processing techniques for digital communication through dispersive unknown channels. The research undertaken has been principally aimed at the analytical derivations of an adaptive recursive filter and an adaptive recursive equalizer, and the simulations of overall binary communication systems, taking into account dispersive effects as well as random noise.

Computer simulation tests have indicated that the new adaptive equalizer exhibits a much more robust operation capability and improved system performance than the conventional adaptive equalizer. This study has indicated that adaptive signal processing is a viable technique upon which a reliable communications system may be designed.