Signal Design for RC Matched Filters

In designing systems using matched filters constructed from passive networks, it is often advantageous to know the properties of the signals that may be matched using particular types of passive filters and noise correlation functions, but such a general classification is difficult. Some previous results on the "positiveness" of functions, however, suggest a possible basis for this classification. In this correspondence some preliminary consideration is given to a formulation of this approach with the prime objective of designing matching signals. When the matched filter is constructed from a certain class of
RC
networks, it is shown that the positivity of the signal can be directly related to the positivity of the noise correlation function. For noise processes typically encountered in practice, the positiveness of the correlation function can in fact be determined, which leads to some useful statements concerning the signal functions that may be used with such filters.