Simplified equations to generate wavelets of arbitrary order of regularity
Addison B. Jump, B.G. Sherlock · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2001
This research deals with finite length, perfect reconstruction two-channel orthonormal wavelet filters. We have previously derived equations that allow the user to set the regularity of these filters to any value between one and the maximum possible. These equations were extremely involved and intricate. We derive identities that greatly simplify the equations and reduced computational complexity. We indicate how the equations may be used to find the optimum filter for a particular application over a pool of filters of regularity set by the user. We advance conjectures as to the theoretical significant of the structure of these equations and discuss numerical solutions.