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Introduction to wavelets in engineering
Author(s) -
Williams John R.,
Amaratunga Kevin
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620371403
Subject(s) - wavelet , legendre wavelet , daubechies wavelet , lifting scheme , discrete wavelet transform , computer science , wavelet transform , fast wavelet transform , multiresolution analysis , second generation wavelet transform , wavelet packet decomposition , mathematics , cascade algorithm , algorithm , artificial intelligence
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 provide extensive details of the derivation of Mallat's transform and Daubechies' wavelet coefficients, since these are fundamental to gaining an insight into the properties of wavelets. The potential benefits of using wavelets are highlighted by presenting results of our research in one‐ and two‐dimensional data analysis and in wavelet solutions of partial differential equations.