This paper describes a novel approach to automatic channel equalization in digital transmission systems. The approach is based on the use of a finite-dimensional rational approximation to the channel characteristics. This class of channel approximation has the following advantages: it allows a finite parametrization of the channel impulse response which may be of infinite duration, it allows for the possibility of the noise being colored, it applies to either single- or multiple-channel systems, and it has the pedigogical advantage that many other algorithms in current use are based on models which are special cases of this model. The rational approximation to the channel characteristics is used in the paper to develop a new receiver structure using fixed-lag smoothing ideas. Simulation studies are presented showing that the receiver offers advantages over other algorithms for mitigating the effects of intersymbol and interchannel interference including those arising from carrier phase errors.