Introduction To Wavelet Transforms
Download Introduction To Wavelet Transforms PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Introduction To Wavelet Transforms book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Wavelet Transforms and Their Applications
Author: Lokenath Debnath
language: en
Publisher: Springer Science & Business Media
Release Date: 2002
Overview Historically, the concept of "ondelettes" or "wavelets" originated from the study of time-frequency signal analysis, wave propagation, and sampling theory. One of the main reasons for the discovery of wavelets and wavelet transforms is that the Fourier transform analysis does not contain the local information of signals. So the Fourier transform cannot be used for analyzing signals in a joint time and frequency domain. In 1982, Jean MorIet, in collaboration with a group of French engineers, first introduced the idea of wavelets as a family of functions constructed by using translation and dilation of a single function, called the mother wavelet, for the analysis of nonstationary signals. However, this new concept can be viewed as the synthesis of various ideas originating from different disciplines including mathematics (Calder6n-Zygmund operators and Littlewood-Paley theory), physics (coherent states in quantum mechanics and the renormalization group), and engineering (quadratic mirror filters, sideband coding in signal processing, and pyramidal algorithms in image processing). Wavelet analysis is an exciting new method for solving difficult problems in mathematics, physics, and engineering, with modern applications as diverse as wave propagation, data compression, image processing, pattern recognition, computer graphics, the detection of aircraft and submarines, and improvement in CAT scans and other medical image technology. Wavelets allow complex information such as music, speech, images, and patterns to be decomposed into elementary forms, called the fundamental building blocks, at different positions and scales and subsequently reconstructed with high precision.
An Introduction to Wavelet Analysis
Author: David F. Walnut
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-12-11
An Introduction to Wavelet Analysis provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and application of wavelet bases. The book develops the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows us to generalize and improve upon the Haar series. Once these ideas have been established and explored, variations and extensions of Haar construction are presented. The mathematical pre-requisites for the book are a course in advanced calculus, familiarity with the language of formal mathematical proofs, and basic linear algebra concepts. Features: *Rigorous proofs with consistent assumptions on the mathematical background of the reader; does not assume familiarity with Hilbert spaces or Lebesgue measure * Complete background material on (Fourier Analysis topics) Fourier Analysis * Wavelets are presented first on the continuous domain and later restricted to the discrete domain, for improved motivation and understanding of discrete wavelet transforms and applications. * Special appendix, "Excursions in Wavelet Theory " provides a guide to current literature on the topic * Over 170 exercises guide the reader through the text. The book is an ideal text/reference for a broad audience of advanced students and researchers in applied mathematics, electrical engineering, computational science, and physical sciences. It is also suitable as a self-study reference guide for professionals. All readers will find
Wavelet Transforms
Author: Raghuveer M. Rao
language: en
Publisher: Pearson Education India
Release Date: 1998
This Book Identifies Problems For Which Wavelet Transform Techniques Are Well-Suited, Shows How To Implement Wavelet Transforms Efficiently, And Explains How To Choose Or Design Appropriate Wavelets For A Given Application. Practical In Their Approach, The Authors Present The Material In A Visual And Comprehensive Manner, Using Geometric Analogies And Filtering Concepts. The Book Is Written In A Language Familiar To Readers With A Basic Undergraduate Engineering Degree.