Spatial-Domain Design of 2-D Quadrantal Symmetric Digital Filters Using Singular-value Decomposition and Singular Perturbation Model Reduction

Abstract

In this paper a new technique is presented to design low order 2-D quadrantally symmetric HR digital filters. This technique is based on two steps: First, the 2-D impulse response specification (Hankel matrix) is decomposed into k parallel sections, each consists of two cascaded SISO 1-D filters, using the singular value decomposition. Second, a singular perturbational model reduction algorithm is applied to the 1- D filter to approximate the N-dimensional FIR into n-dimensional IIR filters, where n < N. The approximation step is based on computing the eigenspaces associated with the large eigenvalues of the cross- Gramian matrix Wco. Examples are given to illustrate the proposed technique.