Theory and Design of Adaptive Filters 

 Published in 1987 by John R. Treichler, C. Richard Johnson Jr., and Michael J. Larimore.

This book is a comprehensive and mathematically rigorous treatment of adaptive filter theory and design, a key area in digital signal processing. It focuses on systems that automatically adjust their parameters in response to changing input signals and environments.

The text begins with foundational concepts in linear systems, random processes, and signal modeling, providing the theoretical background necessary to understand adaptive filtering. It then introduces the principles of estimation and optimization, which underpin adaptive algorithms.

A central focus of the book is the development and analysis of major adaptive filtering algorithms, including:

Least Mean Squares (LMS) algorithms
Recursive Least Squares (RLS) methods
Gradient-based adaptation techniques

The authors examine these algorithms in detail, covering convergence behavior, stability, computational complexity, and performance trade-offs. Mathematical derivations are emphasized to provide a deep understanding of how and why the algorithms work.

The book also explores practical design considerations, such as:

Finite precision effects and implementation issues
Tracking performance in nonstationary environments
Noise and interference handling

Applications discussed include:

Echo and noise cancellation
System identification
Channel equalization in communications systems