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 least-mean-square (LMS) adaptive filter and the normalized LMS adaptive filter that implements the system model using the parallel-cascade 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.