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.

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.

Reviewer: Vjatscheslav Vasiliev (Tomsk)

##### MSC:

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 |