Abstract: The determination of equivalent systems both in time domain and frequency domain is discussed. Various matching forms of equivalent systems are studied. In frequency domain, the non-linear optimization is used to find out the equivalent parameters. In time domains the adaptive filtering algorithms with UD decomposition are employed as an identification algorithm to estimate the parameters. Some new results about the mismatching criterion, single and double matching, time delay and equivalence base are given. They are proved by digital computing and real-time microprocessor realization.