## A Wavelet Tour of Signal ProcessingThis book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École Polytechnique in Paris. Key Features * Provides a broad perspective on the principles and applications of transient signal processing with wavelets * Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms * Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements * Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet * Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition * Optical flow calculation and video compression algorithms * Image models with bounded variation functions * Bayes and Minimax theories for signal estimation * 200 pages rewritten and most illustrations redrawn * More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics |

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It is a mathematically well-organized book on wavelet theories. Also, it well explains the most important theories such as wavelet zooming with beautiful language. I am perfectly satisfied with it.

#### Review: A Wavelet Tour of Signal Processing

User Review - Galal - GoodreadsVery good book for the basics and suitable for the beginners . Read full review

### Contents

1 | |

20 | |

42 | |

CHAPTER IV TIME MEETS FREQUENCY | 67 |

CHAPTER V FRAMES | 125 |

CHAPTER VI WAVELET ZOOM | 163 |

CHAPTER VII WAVELET BASES | 220 |

CHAPTER VIII WAVELET PACKET AND LOCAL COSINE BASES | 321 |

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### Common terms and phrases

algorithm amplitude approximation error best basis biorthogonal wavelet bounded variation calculated circular convolution compact support computed conjugate mirror ﬁlters constructed converges cosine bases covariance Daubechies decay decomposed decomposition deﬁned derive diagonal dictionary Dirac discrete Fourier discrete Fourier transform discrete signal distortion rate dyadic wavelet transform efﬁcient energy Figure ﬁlter ﬁlter bank ﬁlter h ﬁnd ﬁnite ﬁrst following theorem frame Gaussian implies inﬁnite inner products instantaneous frequency interpolation intervals inverse linear log2 matching pursuit minimax minimax risk minimizes modulus maxima multiresolution multiscale noise non-linear approximation non-zero obtained operator optimal orthogonal basis orthonormal basis piecewise pixels polynomial Proof properties Proposition proves quantization reconstruction sampling satisﬁes scale 21 scaling functions Section shows signal f signiﬁcance singularities space spline stationary process sufﬁcient thresholding estimator time-frequency transform code translation invariant tree vanishing moments vectors verify WAVELAB wavelet basis wavelet coefﬁcients wavelet packet basis Wigner-Ville distribution windowed Fourier transform zero