Transmitter and Receiver Filters for Digital PAM Using Transversal Filters with Few Taps

Optimization in the mean-square sense of a transmitter and receiver filter for a time-discrete pulse-amplitude modulation (PAM) system is considered, assuming a situation of realizable filters. This means a general departure from the common matched filter-periodic filter receiver structure. The minimization is carried out with respect to both intersymbol interference and noise, assuming that both transmitter and receiver filters consist of a limited number of basic filters. It is shown that, in general, few basic filters need to be used and that, in general, it is inefficient to use a matched filter and equalizer as a receiver if the transmitter filter is not optimized.