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**A wavelet tour of signal processing.**
*(English)*
Zbl 0937.94001

San Diego, CA: Academic Press. xxiv, 577 p. (1998).

Wavelet methods have found many important applications in signal processing during the last few years. The book provides a broad perspective on the principles and applications of transient signal processing with wavelets. It is a graduate textbook written for students and researchers in electrical engineering, computer science, and applied mathematics. Numerous examples of applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements are given. The author has made important contributions to wavelet signal processing.

The book consists of 11 chapters, 2 appendices, a bibliography (with 316 references), and a subject index. Chapter 1 gives an overview of the contents. Fourier analysis and time-invariant signal processing are reviewed in Chapters 2 and 3. The important concept of local time-frequency decomposition is discussed in Chapter 4. Then in Chapter 5, frames are introduced as flexible tools that are useful for understanding the properties of nonlinear representations. Zooming properties of the wavelet transform are described in Chapter 6. Orthogonal and biorthogonal wavelet bases are discussed in Chapter 7. Then Chapter 8 on wavelet packets and local cosine bases introduces different orthogonal tilings of the time-frequency plane. Linear and nonlinear approximation in wavelet bases are covered in Chapter 9. An application to signal estimation with wavelet thresholding is given in Chapter 10. Finally in Chapter 11, image transform codes in wavelet bases are presented. Appendix A is devoted to mathematical supplements and Appendix B to WAVELAB, which is a MATLAB toolbox for wavelet signal processing.

Not all theorems are proved in detail, but the important techniques are included. Numerical algorithms and figures escort most results. The use of WAVELAB makes it easy to include numerical simulations on one’s own. Problems are listed at the end of each chapter.

This important book will serve as a Bible for anyone concerned with applications of wavelets to signal processing.

The book consists of 11 chapters, 2 appendices, a bibliography (with 316 references), and a subject index. Chapter 1 gives an overview of the contents. Fourier analysis and time-invariant signal processing are reviewed in Chapters 2 and 3. The important concept of local time-frequency decomposition is discussed in Chapter 4. Then in Chapter 5, frames are introduced as flexible tools that are useful for understanding the properties of nonlinear representations. Zooming properties of the wavelet transform are described in Chapter 6. Orthogonal and biorthogonal wavelet bases are discussed in Chapter 7. Then Chapter 8 on wavelet packets and local cosine bases introduces different orthogonal tilings of the time-frequency plane. Linear and nonlinear approximation in wavelet bases are covered in Chapter 9. An application to signal estimation with wavelet thresholding is given in Chapter 10. Finally in Chapter 11, image transform codes in wavelet bases are presented. Appendix A is devoted to mathematical supplements and Appendix B to WAVELAB, which is a MATLAB toolbox for wavelet signal processing.

Not all theorems are proved in detail, but the important techniques are included. Numerical algorithms and figures escort most results. The use of WAVELAB makes it easy to include numerical simulations on one’s own. Problems are listed at the end of each chapter.

This important book will serve as a Bible for anyone concerned with applications of wavelets to signal processing.

Reviewer: M.Tasche (Rostock)

### MSC:

94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |

42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |

65T60 | Numerical methods for wavelets |

94-02 | Research exposition (monographs, survey articles) pertaining to information and communication theory |