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**Adaptive filter theory.
2nd ed.**
*(English)*
Zbl 0723.93070

Prentice Hall Information and System Sciences Series. Englewood Cliffs, NJ etc: Prentice Hall International, Inc. xx, 854 p. $ 39.95 (1991).

The second edition of this well-known book has more than 250 pages in addition to the first edition, and many parts of the old text have been rewritten. A brief description of the contents of this book and of the main improvements in the second edition follows.

Chap. 1 introduces the adaptive filtering problem and its applications. In the new edition, the section on applications has been expanded and new material on filter structures and cost functions has been added. Chaps. 3 through 4 present basic results on discrete-time stationary stochastic processes and correspond to Chap. 2 in the 1st edition; with Chapt. 3 and 4 containing new material on spectrum analysis and eigenanalysis, respectively. Chaps. 5 through 7 done with Wiener filters, linear prediction and Kalman filters, respectively. They have been reorganized but do not differ too much from their predecessors. The subject of Chaps. 8 to 18 is linear FIR adaptive filtering. Chaps. 8 and 9 describe adaptive trasversal filters based on gradient estimation and are obtained by expanding and then splitting Chap. 5 in the old edition. Chaps. 10 and 11, on the least-squares method and its implementation by means of singular value decomposition (SVD), correspond to the old Chap. 7. Much of the material on SVD in Chap. 11 is new. Chap. 12, on eigenvector-based super-resolution algorithms also contains a wealth of new material. Chaps. 13 through 18 discuss the standard recursive least-squares (RLS) method and its fast implementation algorithms. Chaps. 13, 15 and 16 describe the RLS algorithm and its fast implementation in transverse form, and are obtained by expanding the material in the old Chap. 8 Chap. 14, on systolic arrays implementaion of RLS, correspond to the old Chap. 10, whereas Chap. 17 on RLS lattice filters to the old Chap. 9. Chap. 18 on QR decomposition-based LS lattices is new. The last those chapters of the book, on finite-precision effects (Chap. 19), blind deconvolution (Chap. 20) and explored and unexplored topics (Chap. 21) are to be found in the 2nd edition only. The book ends with several appendices, a glossary, an extensive bibliography and a subject index. To conclude, then the second edition of this established title looks as a new book in many respects, and it is highly recommended to able those who study the beautiful subject of adaptive filtering.

Chap. 1 introduces the adaptive filtering problem and its applications. In the new edition, the section on applications has been expanded and new material on filter structures and cost functions has been added. Chaps. 3 through 4 present basic results on discrete-time stationary stochastic processes and correspond to Chap. 2 in the 1st edition; with Chapt. 3 and 4 containing new material on spectrum analysis and eigenanalysis, respectively. Chaps. 5 through 7 done with Wiener filters, linear prediction and Kalman filters, respectively. They have been reorganized but do not differ too much from their predecessors. The subject of Chaps. 8 to 18 is linear FIR adaptive filtering. Chaps. 8 and 9 describe adaptive trasversal filters based on gradient estimation and are obtained by expanding and then splitting Chap. 5 in the old edition. Chaps. 10 and 11, on the least-squares method and its implementation by means of singular value decomposition (SVD), correspond to the old Chap. 7. Much of the material on SVD in Chap. 11 is new. Chap. 12, on eigenvector-based super-resolution algorithms also contains a wealth of new material. Chaps. 13 through 18 discuss the standard recursive least-squares (RLS) method and its fast implementation algorithms. Chaps. 13, 15 and 16 describe the RLS algorithm and its fast implementation in transverse form, and are obtained by expanding the material in the old Chap. 8 Chap. 14, on systolic arrays implementaion of RLS, correspond to the old Chap. 10, whereas Chap. 17 on RLS lattice filters to the old Chap. 9. Chap. 18 on QR decomposition-based LS lattices is new. The last those chapters of the book, on finite-precision effects (Chap. 19), blind deconvolution (Chap. 20) and explored and unexplored topics (Chap. 21) are to be found in the 2nd edition only. The book ends with several appendices, a glossary, an extensive bibliography and a subject index. To conclude, then the second edition of this established title looks as a new book in many respects, and it is highly recommended to able those who study the beautiful subject of adaptive filtering.

Reviewer: P.Stoica (Bucureşti)

### MSC:

93E11 | Filtering in stochastic control theory |

93C40 | Adaptive control/observation systems |

93C55 | Discrete-time control/observation systems |

93-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |