Elliptic-cylindrical wavelets: the Mathieu wavelets

Author

Lira, M.M.S. ; de Oliveira, H.M. ; Cintra, R.Jd.S.

Author_Institution

Power Syst. Digital Lab., Fed. Univ. of Pernambuco, Recife, Brazil

Volume

11

Issue

1

fYear

2004

Firstpage

52

Lastpage

55

Abstract

This note introduces a new family of wavelets and a multiresolution analysis that exploits the relationship between analyzing filters and Floquet´s solution of Mathieu differential equations. The transfer function of both the detail and the smoothing filter is related to the solution of a Mathieu equation of the odd characteristic exponent. The number of notches of these filters can be easily designed. Wavelets derived by this method have potential application in the fields of optics and electromagnetism.

Keywords

differential equations; filtering theory; smoothing methods; transfer functions; waveguide theory; wavelet transforms; Floquet´s solution; Mathieu differential equations; Mathieu wavelets; electromagnetism; elliptic-cylindrical wavelets; multiresolution analysis; odd characteristic exponent; optics; smoothing filter; transfer function; waveguide problems; Differential equations; Horn antennas; Microstrip antennas; Optical distortion; Optical filters; Optical waveguide theory; Optical waveguides; Power harmonic filters; Power system harmonics; Vibrations;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2003.819341

Filename

1255923