ABSTRACT
The discrete Volterra series is one of the powerful tools used in analysis of nonlinear digital systems. In this book, we present its application to nonlinear echo cancellation. Presentation of solutions of nonlinear echo cancellers is, however, preceded by theoretical material in this chapter. This material is necessary for understanding of an analysis presented in the next chapter. The first chapter is long and seems maybe to be partly very advanced because of the usage of functional analysis. The range of functional analysis applied here is, however, needed for explanation and solving of some problems related with the discrete Volterra series, such as its convergence, approximation of a digital nonlinear system by the discrete Volterra series, and so on. All the fundamental notions of functional analysis used are fully explained and illustrated by examples. It is assumed to do this at the place of their first occurrence in the text. No special appendices are devoted to them. The functional analysis allows us to present many known results in a more general framework, as well as to present the recent achievements in the field, which are inherently related to the use of this analysis.
