M. M. S. Lira

M. M. S. Lira, H. M. de Oliveira, M. A. Carvalho et al.

A new family of wavelets is introduced, which is associated with Legendre polynomials. These wavelets, termed spherical harmonic or Legendre wavelets, possess compact support. The method for the wavelet construction is derived from the association of ordinary second order differential equations with multiresolution filters. The low-pass filter associated with Legendre multiresolution analysis is a linear phase finite impulse response filter (FIR).

M. M. S. Lira, H. M. de Oliveira, R. J. Cintra et al.

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 analysing filters can be easily designed. Wavelets derived by this method have potential application in the fields of optics, microwaves and electromagnetism.