Introduction

This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book reviews recursive filter structures, the basic elements that are to be adapted with the available signals. It focuses in particular on the direct form and the tapped-state normalized lattice. The book presents some identification criteria for linear systems by way of the Beurling-Lax theorem and Hankel forms. It lends insight into approximation properties for the undermodelled case as well. The book reviews the rational approximation problem in Hankel norm, following the celebrated work of Adamjan, Arov, and Krein. It presents stability theory for time-varying recursive filters. The book exposes the properties of the transfer functions sought by recursive gradient method by way of interpolation theory, and indicates connections with model reduction. It examines candidate convergent points for the undermodelled case in terms of interpolation conditions.