Wavelet

This book presents a systematic study of multivariate wavelet frames with matrix dilation, in particular, orthogonal and bi-orthogonal bases, which are a special case of frames. Further, it provides algorithmic methods for the construction of dual and tight wavelet frames with a desirable approximation order, namely compactly supported wavelet frames, which are commonly required by engineers.

This book offers an introduction to wavelet theory and provides the essence of wavelet analysis – including Fourier analysis and spectral analysis; the maximum overlap discrete wavelet transform; wavelet variance, covariance, and correlation – in a unified and friendly manner. It aims to bridge the gap between theory and practice by presenting substantial applications of wavelets in economics and finance.

An "applications first" approach to discrete wavelet transformations
Discrete Wavelet Transformations provides readers with a broad elementary introduction to discrete wavelet transformations and their applications. With extensive graphical displays, this self-contained book integrates concepts from calculus and linear algebra into the construction of wavelet transformations and their various applications, including data compression, edge detection in images, and signal and image denoising.

Employs a Step-by-Step Modular Approach to Structural Modeling. Considering that wavelet transforms have also proved useful in the solution and analysis of engineering mechanics problems, up to now there has been no sufficiently comprehensive text on this use. Wavelet Methods for Dynamical Problems: With Application to Metallic, Composite and Nano-composite Structures addresses this void, exploring the special value of wavelet transforms and their applications from a mechanical engineering perspective. It discusses the use of existing and cutting-edge wavelet methods for the numerical solution of structural dynamics and wave propagation problems in dynamical systems…