Title :
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
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;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2003.819341
