## Wavelets: An Elementary Treatment of Theory and ApplicationsNowadays, some knowledge of wavelets is almost mandatory for mathematicians, physicists and electrical engineers. The emphasis in this volume, based on an intensive course on Wavelets given at CWI, Amsterdam, is on the affine case. The first part presents a concise introduction of the underlying theory to the uninitiated reader. The second part gives applications in various areas. Some of the contributions here are a fresh exposition of earlier work by others, while other papers contain new results by the authors. The areas are so diverse as seismic processing, quadrature formulae, and wavelet bases adapted to inhomogeneous cases. |

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### Contents

Preface | 1 |

Mathematical Preliminaries | 13 |

The Continuous Wavelet Transform | 27 |

Discrete Wavelets and Multiresolution Analysis | 49 |

Image Compression using Wavelets | 81 |

Computing with Daubechies Wavelets | 93 |

107 | |

Conjugate Quadrature Filters for Multiresolution Analysis and Synthesis | 129 |

Calculation of the Wavelet Decomposition using Quadrature Formulae | 139 |

Fast Wavelet Transforms and CalderonZygmund Operators | 161 |

The Finite Wavelet Transform with an Application to Seismic Processing | 183 |

Wavelets Understand Fractals | 209 |

### Other editions - View all

Wavelets: An Elementary Treatment of Theory and Applications T. H. Koornwinder No preview available - 1993 |

### Common terms and phrases

algorithm approximation Argoul bases basic wavelet calculate compact compactly supported compactly supported wavelets compute condition consider construction continuous wavelet transform convergence convolution Daubechies decomposition defined definition denote described dilation equation discrete wavelet transform Elementary Treatment equal example Fast wavelet transforms Figure filter Fourier transform fractal frequency given Grossmann Haar Haar measure Haar wavelet Heisenberg group Hence Hilbert space image compression inner product interval inverse isometry kernel Koornwinder Lemma linear Mallat Math mathematical matrix Meyer Morlet mother wavelet multiresolution analysis nonzero norm notation obtained Ondelettes operator orthogonal orthonormal basis paper parameters point quadrature formula polynomial positive constant Proof properties reconstruction representation result Riesz basis satisfies scaling function seismic sequence signal splines square integrable subband coding subspace Tchamitchian Theorem tight frame Treatment of Theory values vector Vj+i wavelet basis wavelet coefficients zero