Elliptic-Cylindrical Wavelets: The Mathieu Wavelets
M. M. S. Lira, Student Member, H. M. De Oliveira, Renato J. Cintra, Student Member · 2015
Abstract—This note introduces a new family of wavelets and a multiresolution analysis that exploits the relationship between an-alyzing filters and Floquet’s solution of Mathieu differential equa-tions. 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. Index Terms—Floquet’s theorem, Mathieu equation, wave-guides, wavelets.