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A Primer on Wavelets and Their Scientific Applications / Edition 1

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The rapid growth of wavelet applications-speech compression and analysis, image compression and enhancement, and removing noise from audio and images-has created an explosion of activity in creating a theory of wavelet analysis and applying it to a wide variety of scientific and engineering problems. It becomes important, then, that engineers and scientists have a working understanding of wavelets. Until now, however, the study of wavelets has been beyond the mathematical grasp of many who need this understanding. Most treatments of the subject involve ideas from functional analysis, harmonic analysis, and other difficult mathematical techniques.

Wavelets and their Scientific Applications offers an introduction to wavelet analysis without mathematical rigor, requiring only algebra and some very basic calculus. The author stresses applications, and explains, using elementary algebra, how wavelet methods are typically applied in analyzing digital data.

Software is available for download through CRC's Website that will enable recording, playing, and modifying sound files, and includes a facility for displaying, printing and modifying IEEE gray field images. Unlike other software packages for wavelet analysis, the author developed this attractive, easy-to-use software without the need for a C++ compiler or MATLABä. Throughout the book the author provides numerous suggestions for computer experiments designed to challenge and enhance the reader's comprehension and provide practice in applying the concepts learned.

Wavelets and their Scientific Applications thus provides the perfect vehicle for understanding wavelets and their uses. It provides a fast-track learning opportunity for scientists and mathematicians unfamiliar with wavelet concepts and applications, and it is ideal for anyone without an extensive mathematical background.

"...offers an introduction to wavelet analysis without mathemataical rigor, requiring only algebra & some basic calculus. The author stresses applications & explains how wavelet methods are typically applied in analyzing data."

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Editorial Reviews

An introduction to wavelet analysis without mathematical rigor, requiring only algebra and some basic calculus. Focus is on applications in analyzing digital data, with enough theoretical background to understand ideas behind fundamental applications of wavelets. Coverage includes speech compression and analysis, image compression and enhancement, and removing noise from audio and images. Includes exercises and experiments. A web site provides software discussed in the book, for recording, displaying, modifying, and printing IEEE gray field images without a C++ compiler or MATLAB. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780849382765
  • Publisher: Taylor & Francis, Inc.
  • Publication date: 3/26/1999
  • Series: Studies in Advanced Mathematics Series
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 168
  • Product dimensions: 6.00 (w) x 9.00 (h) x 0.60 (d)

Table of Contents

1 Haar Wavelets 1
1.1 The Haar transform 1
1.2 Conservation and compaction of energy 6
1.3 Haar wavelets 10
1.4 Multiresolution analysis 13
1.5 Compression of audio signals 18
1.6 Removing noise from audio signals 23
1.7 Notes and references 28
2 Daubechies wavelets 29
2.1 The Daub4 wavelets 29
2.2 Conservation and compaction of energy 38
2.3 Other Daubechies wavelets 42
2.4 Compression of audio signals 49
2.5 Quantization, entropy, and compression 53
2.6 Denoising audio signals 58
2.7 Two-dimensional wavelet transforms 65
2.8 Compression of images 72
2.9 Fingerprint compression 75
2.10 Denoising images 79
2.11 Some topics in image processing 87
2.12 Notes and references 92
3 Frequency analysis 95
3.1 Discrete Fourier analysis 95
3.2 Definition of the DFT and its properties 98
3.3 Frequency description of wavelet analysis 103
3.4 Correlation and feature detection 108
3.5 Object detection in 2D images 114
3.6 Creating scaling signals and wavelets 118
3.7 Notes and references 122
4 Beyond wavelets 123
4.1 Wavelet packet transforms 123
4.2 Applications of wavelet packet transforms 126
4.3 Continuous wavelet transforms 129
4.4 Gabor wavelets and speech analysis 134
4.5 Notes and references 138
A Software for wavelet analysis 139
References 145
Index 151
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  • Anonymous

    Posted July 27, 2002

    The mathematical ideas and the software.

    This lovely little book helps the novice to get an idea of the math behind wavelets, and at the same time to learn how one readily gets hold of software that is convinient, that will make it easy for anyone to start playing around with it. It also explains in plain English the wavelet aspects of audio denoising, signal compression, image recognition, speech recognition and more.

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