• Adaptive Filter Theory (4th Edition)
• Adaptive Filtering Primer with MATLAB
• Fundamentals of Adaptive Filtering
• Fundamentals of Statistical Processing, Volume I: Estimation Theory (Prentice Hall Signal Processing Series)
• Intuitive Probability and Random Processes using MATLAB

Good but...
Review written by: A. santamaria From ca
This book can only be read if you have a very strong background in mathematics. Adaptive filter design is a career on its own, you need a good instructor in order to understand it. If your math is moderate, this book will not help and you will be wasting your money but If your math is great then you might consider buying it.

Best book for learning adaptive signal processing
Review written by: calvinnme From Fredericksburg, Va
Adaptive signal processing is akin to neural networks in that they are both non-linear solutions to problems. In traditional linear modeling approaches, it is possible to algorithmically determine the model configuration that absolutely minimizes output error. The price paid for the greater non-linear modeling power of neural networks and adaptive filters is that although we can adjust a network to lower its error, we can never be sure that the error could not be lower still.
This book, although over twenty years old, is still the best one on the subject in my opinion. The book first introduces the concept of the adaptive linear combiner in which the weights of a weighted sum are updated based on the output of an adaptive algorithm that uses the difference between the output of the weighted sum and the filter's output along with the inputs that are being weighted. In essence, an adaptive filter is forming the weights of a neural network.
The next section of the book deals with the underlying assumptions about the statistics of the input signals to adaptive systems along with the extremely large time complexity (O(n^3)) required to solve for an adaptive system per iteration. This is largely due to the inversion of an NxN autocorrelation matrix that must be done per iteration. It is demonstrated that this time complexity can be reduced by using the concept of the performance surface and gradient estimation. This method adapts the filter coefficients on a sample-by-sample basis by using the steepest descent method in which the next filter coefficient "vector" h(n+1) is increased by a change proportional to the negative gradient of the mean-square-error performance surface. In this section of the book, knowledge of random processes is essential and knowledge of the theory of algorithms would be helpful.
Next the book talks specifically about the least mean squares algorithm, which is the basis for solving adaptive systems, along with the role of the Z-transform in adaptive systems and their description.
The final part of the book talks about the various applications of adaptive filters and how they are used to solve real problems. The first and simplest application shown is that of system identification. The author clearly shows how to set up an adaptive system that is parallel to the unknown system. Changing the adaptive system's filter taps until the difference between the output of the unknown and adaptive systems is minimal yields the filter coefficients for the unknown system. The author uses this basic example to branch off into more difficult problems such as equalization and beamforming.
I found the text to be very clear and well illustrated with many worked out examples. However, an absolute minimum requirement for understanding this book would be a course or equivalent experience in both random processes and digital signal processing. The following is the table of contents:
GENERAL INTRODUCTION.
Adaptive Systems.
The Adaptive Linear Combiner.
THEORY OF ADAPTATION WITH STATIONARY SIGNALS.
Properties of the Quadratic Performance Surface.
Searching the Performance Surface.
Gradient Estimation and Its Effects on Adaptation.
ADAPTIVE ALGORITHMS AND STRUCTURES.
The LMS Algorithm.
The Z-Transform in Adaptive Signal Processing.
Other Adaptive Algorithms and Structures.
Adaptive Lattice Filters.
APPLICATIONS.
Adaptive Modeling and System Identification.
Inverse Adaptive Modeling, Deconvolution, and Equalization.
Adaptive Control Systems.
Adaptive Interference Cancelling.
Introduction to Adaptive Arrays and Adaptive Beamforming.
Analysis of Adaptive Beamformers.

Classic
This is a classic not because it was one of the first books on the subject but because he actually lets you "understand".

I have not found a comperable book on Kalman filtering. To bad Widrow and Stearns have not written one on this subject.

Get This Book if you want to get This Subject.
Review written by: Mr. Roy B. Mccammon From Austin, TX United States
I've even been known to give this book as a gift (for the electrical engineer that doesn't have everything). Something that I have observed about superior explainers over the years, is that if they really know the subject, then they can explain it to almost anyone. Widrow invented the subject and can see it with his mind's eye and more importantly can give you the vision. He reduces the dynamics to a marble seeking the bottom of a bowl. In fact, he helps you become the marble and the bowl. I have attended many seminars and short classes over the years at UCLA. Widrow's was the only one where we gave the lecturer a standing ovation.

Before I read this book, adaptive filtering was a mystery and the LMS algorithm looked like a programming nightmare. It looked like more Kalman filtering. My eyes have been opened. The LMS algorithm for adaptive filtering is almost as simple as Tit for Tat is for game theory. This is the gateway text to understand adaptive filtering, adaptive arrays (help the navy find the rogue submarine), adaptive equalization (design the next generation of modem), adaptive control (say goodbye to overshoot), adaptive prediction (beat the stock market). Furthermore, it leads naturally into the artificial intelligence techniques.

If you are an engineer or a programmer, you should have this tool in your toolbox.

The best introductory book I've seen on this subject
Review written by: Richard B. Wells From University of Idaho, Moscow, Idaho
This book is for the person who actually wants to learn HOW IT WORKS. Widrow writes in a clear and easy-to-follow style which delivers all of the mathematical theory and detail of the process of adaptation without drowning the reader in formalism. Statistical signal processing, adaptation dynamics, steady-state behavior, performance - this book explains all of these fundamentals. If you want to become an expert in adaptive signal processing, start with this book.