Wavelet theory and its applications (original) (raw)
Related papers
Introduction to Wavelets in Engineering
The aim of this paper is to provide an introduction to the subject of wavelet analysis for engineering applications. The paper selects from the recent mathematical literature on wavelets the results necessary to develop wavelet based numerical algorithms. In particular, we p r o vide extensive details of the derivation of Mallat's transform and Daubechies' wavelet coe cients, since these are fundamental to gaining an insight i n to the properties of wavelets. The potential bene ts of using wavelets are highlighted by presenting results of our research in one and two dimensional data analysis and in wavelet solutions of partial di erential equations.
Trends in Wavelet Applications
Lecture Notes in Pure and Applied Mathematics, 2005
The study of wavelet analysis which was formally developed in the late 1980s has progressed very rapidly. There exists a vast literature on its applications to image processing and partial differential equations. However, Black-Scholes equation of pricing, Maxwell's equations, variational inequalities, and complex dynamic optimization problems related to real-world phenomena are some of the areas where applications of wavelet methods have not been fully explored. Wavelet packet analysis which includes wavelet analysis as a special case has wide scope for further research from both theoretical and applied viewpoints. As we know, wavelet methods are refinements of Fourier analysis, finite element, and boundary element meth-125
Wavelet analyses and applications
European Journal of …, 2009
It is shown how a modern extension of Fourier analysis known as wavelet analysis is applied to signals containing multiscale information. First, a continuous wavelet transform is used to analyse the spectrum of a nonstationary signal (one whose form changes in time). The spectral analysis of such a signal gives the strength of the signal in each frequency as a function of time. Next, the theory is specialized to discrete values of time and frequency, and the resulting discrete wavelet transform is shown to be useful for data compression. This paper is addressed to a broad community, from undergraduate to graduate students to general physicists and to specialists in other fields than wavelets.
1993
The past ten years have seen an explosion of research in the theory of wavelets and their applications. Theoretical accomplishments include development of new bases for many different function spaces and the characterization of orthonormal wavelets with compact support. Applications span the fields of signal processing, image processing and compression, data compression, and quantum mechanics. At the present time however, much of the literature remains highly mathematical, and consequently, a large investment of time is often necessary to develop a general understanding of wavelets and their potential uses. This paper thus seeks to provide an overview of the wavelet transform from an intuitive standpoint. Throughout the paper a signal processing frame of reference is adopted.