Frequency-domain realizations of adaptive parallel-cascade quadratic filters

Parallel-cascade realizations of truncated Volterra systems implement higher-order systems using a parallel connection of multiplicative combinations of lower-order systems. Such realizations are modular and permit efficient approximations of truncated Volterra systems. Frequency-domain realizations of the leastmean-square (LMS) adaptive filter and the normalized LMS adaptive filter that implements the system model using the parallelcascade structure are presented in this paper. Computational complexity analysis and simulation results show that the normalized frequency-domain, parallel-cascade LMS adaptive quadratic filter has the advantages of computational simplicity and superior performance over direct form realizations.