Efficient block-adaptive parallel-cascade quadratic filters

This brief presents computationally efficient block-adaptive algorithms for quadratic filters employing parallel-cascade realizations of the system model. Parallel-cascade realizations implement higher order Volterra systems using a parallel connection of multiplicative combinations of lower order systems. Such realizations are modular and therefore well-suited for very large scale integrate circuit implementation. They also permit efficient approximations of truncated Volterra systems. Mixed frequency- and time-domain realizations of the least-mean-square (LMS) adaptive filter, as well as that of a normalized LMS adaptive filter, are presented in this brief. The adaptive normalized LMS parallel-cascade quadratic filter has the advantages of computational simplicity and superior performance over its direct form, and unnormalized adaptive parallel-cascade counterparts.