Elliptic-cylindrical wavelets: the Mathieu wavelets

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.