2004/01/01 by M. M. S. Lira, M.M.S. Lira, H. M. de Oliveira +3
Computer Science · Mathematics · #Differential equation #Digital Filter Design and Implementation #Filter (signal processing) #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Mathieu function #Multiresolution analysis #Smoothing #Transfer function #Wavelet #cs.NA #math.NA #stat.AP #stat.ME
paper · pdf · doi:10.1109/lsp.2003.819341
published as IEEE Signal Processing Letters, vol. 11, issue 1, pp. 52-55, 2004 · 10 pages, 2 figures
openalex publication_date 2004/01/01 · arxiv created 2015/01/28 · arxiv updated 2015/01/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.