Recursive filters determined from implicit formulations

Abstract

A numerical procedure is used to identify the relationship between recursive and implicit filters. We find that the implicit filters can each be decomposed into two recursive filters at each grid point location by using Choleski matrix factorization. Specifically, the implicit second-order sine filter yields the traditional first-order recursive filter, while we recover the standard second-order recursive sine filter from its fourth-order implicit counterpart. This approach thus provides an alternative to traditional methods for calculating the coefficients associated with the recursive sine filters. We also find that we cannot recover the traditional form for the recursive tangent filter from the implicit tangent filter.