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Jensen ISBN: 025 Genre: Mathematics File Size: 23.50 MB Format: PDF, Mobi Download: 951 Read: 726 This introduction to the discrete wavelet transform and its applications is based on a novel approach to discrete wavelets called lifting. After an elementary introduction, connections of filter theory are presented, and wavelet packet transforms are defined. The time-frequency plane is used for interpretation of signals, problems with finite length signals are detailed, and MATLAB is used for examples and implementation of transforms. Category: Mathematics.

The second book under review, Ripples in Mathematics: The Discrete Wavelet Transform, byArne Jensenand Andersla Cour-Harbo, could hardly bemoredifferent. It floats over the mathematical obstacles by keeping everything finite, dropping the heavy machinery needed for infinite series and function spaces. The text grew out of.

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Author: Patrick J. Van Fleet ISBN: 660 Genre: Mathematics File Size: 56.89 MB Format: PDF Download: 514 Read: 252 An 'applications first' approach to discrete wavelettransformations Discrete Wavelet Transformations provides readers with a broadelementary introduction to discrete wavelet transformations andtheir applications. With extensive graphical displays, thisself-contained book integrates concepts from calculus and linearalgebra into the construction of wavelet transformations and theirvarious applications, including data compression, edge detection inimages, and signal and image denoising. The book begins with a cursory look at wavelet transformationdevelopment and illustrates its allure in digital signal and imageapplications. Next, a chapter on digital image basics, quantitativeand qualitative measures, and Huffman coding equips readers withthe tools necessary to develop a comprehensive understanding of theapplications.

Subsequent chapters discuss the Fourier series,convolution, and filtering, as well as the Haar wavelet transformto introduce image compression and image edge detection. Thedevelopment of Daubechies filtersis presented in addition tocoverage of wavelet shrinkage in the area of image and signaldenoising. The book concludes with the construction of biorthogonalfilters and also describes their incorporation in the JPEG2000image compression standard. The author's 'applications first' approach promotes a hands-ontreatment of wavelet transforma-tion construction, and over 400exercises are presented in a multi-part format that guide readersthrough the solution to each problem.

Over sixty computer labs andsoftware development projects provide opportunities for readers towrite modules and experiment with the ideas discussed throughoutthe text. The author's software package, DiscreteWavelets, is usedto perform various imaging and audio tasks, compute wavelettransformations and inverses, and visualize the output of thecomputations. Supplementary material is also available via thebook's related Web site, which includes an audio and videorepository, final project modules, and softwarefor reproducingexamples from the book. All software, including theDiscreteWavelets package, is available for use withMathematica®, MATLAB®, and Maple. Discrete Wavelet Transformations strongly reinforces the use ofmathematics in digital data applications, sharpens programmingskills, and provides a foundation for further study of moreadvanced topics, such as real analysis. This book is ideal forcourses on discrete wavelet transforms and their applications atthe undergraduate level and also serves as an excellent referencefor mathematicians, engineers, and scientists who wish to learnabout discrete wavelet transforms at an elementary level.