Parallel-cascade realizations of truncated Volterra systems

This dissertation presents alternate realizations of a class of nonlinear filters known as truncated Volterra systems. Volterra system models have been successfully employed in a wide variety of applications, and such models continue to be popular among researchers working an nonlinear signal processing. The biggest drawback of Volterra system models is the complexity associated with their implementation. This dissertation presents parallel-cascade structures that can approximate Volterra systems efficiently and thereby reducing their complexity. Adaptive filters based on such structures are also proposed in this dissertation.;Parallel-cascade structures implement truncated Volterra filters based on appropriate matrix decompositions of the coefficient matrix. In such realizations, higher-order Volterra systems are implemented as a parallel system of multiplicative combinations of lower-order Volterra systems. These realizations are modular and they provide a systematic way of approximating Volterra systems. Quantitative measures for the error in approximating Volterra systems using parallel-cascade realizations is derived in this dissertation. Several variations of the parallel-cascade realizations are also proposed in this dissertation.;Adaptive Volterra filters based on parallel-cascade structures are also studied in this dissertation. A normalized Least-Mean-Square adaptive filter for parallel-cascade realizations of Volterra filters is derived in this dissertation. The algorithm is shown to perform better than other competing algorithms through simulation experiments.;A Gauss-Newton type algorithm for parallel-cascade Volterra system is presented in this dissertation. The stability issues of such an algorithm are discussed. An approximate version of the Gauss-Newton type algorithm and the complexity issues associated with it are also discussed in this dissertation.