Modern Applications Of Wavelet Transform
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Modern Applications of Wavelet Transform
Author: Srinivasan Ramakrishnan
language: en
Publisher: BoD – Books on Demand
Release Date: 2024-02-07
This book explores the use of wavelet transforms in signal processing, including image, finance, and communication systems. It covers five contemporary applications, including the interaction between inertial sensors and wavelet filtering techniques, geophysical prospecting, volatility patterns in asset returns, computerized tomography (CT), and fault detection techniques. The book provides a foundation for further exploration, focusing on wavelet transformations' basic principles, their application in geophysical prospecting, and their use in identifying volatility patterns in asset returns. The book is intended for students, researchers, and professionals interested in understanding wavelet transforms and their practical implementations.
Wavelet Transforms and Their Applications
Author: Lokenath Debnath
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-06-28
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.
Multirate and Wavelet Signal Processing
This innovative and in-depth book integrates the well-developed theory and practical applications of one dimensional and multidimensional multirate signal processing. Using a rigorous mathematical framework, it carefully examines the fundamentals of this rapidly growing field. Areas covered include: basic building blocks of multirate signal processing; fundamentals of multidimensional multirate signal processing; multirate filter banks; lossless lattice structures; introduction to wavelet signal processing. Multirate and Wavelet Signal Processing forms the basis for a graduate course in multirate signal processing. It includes an introduction to wavelet signal processing and emphasizes topics of ever-increasing importance for a wide range of applications. Concise and easy-to-read, this book is also a useful primer for professional engineers. - Integrates the well-developed theory and practical applications of one-dimensional and multidimensional multirate signal processing - Emphasizes topics of ever-increasing importance for a wide range of applications - Written in a concise, easy-to-read style - Uses relevant examples - General mathematical formulation permits extensions of concepts to diverse applications, such as speech, imaging, video, and synthetic aperture radar - Emphasizes key topics of the field, allowing the reader to make the most efficient use of time in learning the fundamentals of multirate - Designed to be completely covered in a single semester or quarter