Orthogonal wavelets with applications in electromagnetics

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Abstract

A topic of considerable current interest in applied mathematics is wavelets. The promises of wavelets arc based upon their localization in both spatial and spectral domains, better convergence properties, their computational speed, and the two parameter invariance under analytic representations. Recently Wavelets have been used in signal processing and computer vision with great success. In electromagnetics (EM), orthonormal wavelets have been applied to the method of moments as basis and testing functions in the integral equations to replace the pulse, triangle, and PWS (piecewise sinusoidal) functions. Very sparse coefficient matrices have been obtained due to the vanishing moments, localization, and MRA (multiresolution analysis) of the wavelets. In this paper we introduce the basic wavelet theory, summarize the wavelet properties and present the applications of orthogonal wavelets to the eddy current and EM wave scattering problems.

Original languageEnglish (US)
Pages (from-to)975-983
Number of pages9
JournalIEEE Transactions on Magnetics
Volume32
Issue number3 PART 2
DOIs
StatePublished - Dec 1 1996

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Keywords

  • Fast wavelet transform (FWT)
  • Method of moments (MoM)
  • Multiresolution analysis (MRA)
  • Radar cross-section
  • Wavelet

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Electrical and Electronic Engineering

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