42. Wavelets for Elliptical Waveguide Problems

New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and
Floquet’s solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution
filters is related to the solution of a Mathieu equation of odd characteristic exponent.
The number of notches of these analyzing filters can be easily designed.
Wavelets derived by this method have potential application in the fields of optics, microwaves and electromagnetism.