## A Primer on Wavelets and Their Scientific ApplicationsThe 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. |

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This is a great introduction to wavelets. Things are kept fairly simple, so it's good for getting an idea of how wavelets work and are used, but after reading this you probably still won't be able to read many of the other wavelet books since the math in them gets very heavy.

### Contents

Haar Wavelets 11 The Haar transform | 1 |

12 Conservation and compaction of energy | 6 |

13 Haar wavelets | 10 |

14 Multiresolution analysis | 13 |

15 Compression of audio signals | 18 |

16 Removing noise from audio signals | 23 |

17 Notes and references | 28 |

Daubechies wavelets 21 The Daub4 wavelets | 29 |

Frequency analysis 31 Discrete Fourier analysis | 95 |

32 Definition of the DFT and its properties | 98 |

33 Frequency description of wavelet analysis | 103 |

34 Correlation and feature detection | 108 |

35 Object detection in 2D images | 114 |

36 Creating scaling signals and wavelets | 118 |

37 Notes and references | 122 |

Beyond wavelets 41 Wavelet packet transforms | 123 |

22 Conservation and compaction of energy | 38 |

23 Other Daubechies wavelets | 42 |

24 Compression of audio signals | 49 |

25 Quantization entropy and compression | 53 |

26 Denoising audio signals | 58 |

27 Twodimensional wavelet transforms | 65 |

28 Compression of images | 72 |

29 Fingerprint compression | 75 |

210 Denoising images | 79 |

211 Some topics in image processing | 87 |

212 Notes and references | 92 |

42 Applications of wavelet packet transforms | 126 |

43 Continuous wavelet transforms | 129 |

44 Gabor wavelets and speech analysis | 134 |

45 Notes and references | 138 |

Software for wavelet analysis | 139 |

A1 Description of the books software | 140 |

A2 Installing the books software A3 Other software | 142 |

145 | |

151 | |

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### Common terms and phrases

1-level Daub4 1-level Haar transform 2-level Daub4 transform 2D wavelet abnormal heartbeat acceptance bands analog signal applying approximation audio signals averaged signal chapter Coif6 CoifG CoifSO transform compressed image Continuous wavelet transforms Daub4 wavelet Daubechies wavelet defined denoised signal described detail signal discrete signal discussion encoding entropy equations example FAWAV fc-level fluctuation subsignal fluctuation values Formula frequency content graph Haar wavelets histogram Lena image magnitude Mexican hat wavelet multiple multiresolution analysis noise removal normalized correlation obtained original signal perform produce quantization random noise RMS Error scalar products scaling numbers scaling signals scalogram shown in Figure signal A1 signal f signals and wavelets significance map soft threshold thresholded transform transform of Signal trend subimage trend subsignal trend values values of f Walsh transform wavelet analysis wavelet based wavelet compression wavelet numbers wavelet packet transform wavelet transform compression wavelet Wj z-transform zero zero-tree