This work is concerned with the study of adaptive nonlinear filters and their applications. While the concept of linear filtering has had enormous impact on the development of various techniques for processing stationary and nonstationary signals, there are several applications in which the performance of linear filters is unacceptable. Channel equalization and echo cancellation and echo cancellation in high performance communication systems, image processing, characterization of semiconductor devices, and modeling biological phenomenon are some of the examples of applications in which nonlinear filters have been successfully employed. Possibly because of the computational complexity associated with adaptive nonlinear filters, it is only recently that active research on such systems have begun. The work deals with the following four closely related problems in adaptive nonlinear filtering: 1) Development of efficient algorithms for adaptive nonlinear filters using nonlinearities modeled with finite Volterra series expansions; 2) Development of numerically stable fast recursive least-square Volterra filters based on QR-decomposition techniques; 3) Study of adaptive nonlinear filtering algorithms for systems where the nonlinearity is modeled using recursive, nonlinear difference equations, with relatively few parameters to adequately represent a large class of nonlinearities; and 4) Analytical and empirical performance evaluation of the algorithms developed. These are all challenging and important problems that when solved will result in substantial advances in our nonlinear signal processing capabilities.
