Design of 2-D filters composed of low-order systems

In this paper, we introduce a new analytic approach to the design and analysis of 2-D systems composed of low-order systems used as building blocks. We construct low-order 2-D system functions whose unit-circle root contours can be approximated by a straight line. As a counterpart to a 1-D system function with zeros not on the unit-circle, we introduce the notion of system functions whose magnitude response has, approximately, a constant minimum along a controllable linear contour and show how to construct them. Using these low-order system functions as building blocks, in both cascade and parallel forms, we present a simple and efficient algorithm for designing frequency selective 2-D IIR filters based on summing 2-D all-pass filters