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Adaptive filtering. Algorithms and practical implementation. 4th ed. (English) Zbl 1257.93001
New York, NY: Springer (ISBN 978-1-4614-4105-2/hbk; 978-1-4614-4106-9/ebook). xxi, 652 p. (2013).
The subject of this book is adaptive filtering. Filtering is a signal processing operation whose objective is to process a signal in order to manipulate the information contained in it. For time-invariant filters the internal parameters and the structure of the filter are fixed, and if the filter is linear then the output signal is a linear function of the input signal. An adaptive filter is required when either the fixed specifications are unknown or the specifications cannot be satisfied by time-invariant filters. Adaptive filtering concerns the choice of structures and algorithms for a filter that has its parameters adapted, in order to improve a prescribed performance criterion. The parameter updating is performed using the information available at a given time. As follows, the adaptive filters are time varying since their parameters are continually changing in order to meet a performance requirement.
In the book, the following basic theoretical problems are considered:
- the basic concepts of adaptive filtering are introduced;
- the basic concepts of discrete-time stochastic processes are reviewed with special emphasis on the results that are useful to analyze the behavior of adaptive filtering algorithms. In addition, the Wiener filter is also discussed;
- the Least-Mean-Square (LSM) and related to the LSM algorithms are presented and analyzed. A number of theoretical as well as simulation examples to illustrate the LSM are given;
- the conventional Recursive Least-Squares (RLS) algorithm is introduced. This algorithm minimizes a deterministic objective function, differing in this sense from most LMS-based algorithms. The discrete-time Kalman filter formulation which has some relation with the RLS algorithm is presented;
- some techniques to reduce the overall computational complexity of adaptive filtering algorithms are discussed;
- a family of fast RLS algorithms based on the Finite Impulse Response (FIR) lattice realization is introduced;
- the book addresses also the subject of adaptive filters using Infinite Impulse Response (IIR) digital filter realizations and includes a discussion on how to derive the adaptive algorithms;
- the problem of nonlinear adaptive filtering which consist of utilizing a nonlinear structure for the adaptive filter is considered;
- some adaptive filtering algorithms suitable for situations where no reference signal is available which are known as blind adaptive filtering algorithms are described;
- applications of presented results are discussed.
Moreover, a user-friendly MATLAB package is provided where the reader can easily solve new problems and test algorithms in a quick manner. Additionally, the book provides easy access to working algorithms for practicing engineers.

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93E11 Filtering in stochastic control theory
60G35 Signal detection and filtering (aspects of stochastic processes)
62M20 Inference from stochastic processes and prediction
62P30 Applications of statistics in engineering and industry; control charts
93E10 Estimation and detection in stochastic control theory
93E12 Identification in stochastic control theory
93C40 Adaptive control/observation systems
93C55 Discrete-time control/observation systems
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