Implementation of 2-D Digital Filters by Iterative Methods

摘要

A two-dimensional (2-D) rational filter can be implemented by an iterative computation involving only finite-element impulse response (FIR) filtering operations, provided a certain convergence criterion is met. In this paper, we generalize this procedure so that the convergence criterion is satisfied for any stable 2-D rational transfer function. One formulation which guarantees convergence invokes a relaxed form of the iterative computation along with prefiltering the numerator and denominator polynomials of the rational transfer function. This implementation may be applied with a frequency varying relaxation parameter for increasing the rate of convergence. An alternative generalization uses several previously computed iterates, unlike our first modification which utilizes only the most recently computed iterate. This formulation can potentially guarantee convergence and also increase the convergence rate without the requirement of prefiltering.