A Critical View of Adaptive Filter Theory

In this paper we offer a ”birds eye view” of the field of adaptive filtering with the aim of suggesting a new approach to its teaching. Following a brief survey of the diverse lines of thought underpinning the traditional approach to the presentation of the most common adaptive filter algorithms, we point out that all major families of adaptive filter algorithms can be more easily developed and understood in terms of the well established theory of iterative linear equation solvers. This simplifies both the development and analysis of the most commonly available adaptive filter algorithms and gives additional insight. In particular the commonalities and differences between the various algorithms are more easily understood. This enhanced and complementary understanding, inspired by numerical linear algebra, also paves the way for the conception of new adaptive filter algorithms.