Design of stable two-dimensional IIR filters using digital spectral transformations

In this paper, a new theory is presented for the design of 2-D IIR filters using the transformation
Z = H_1(z_1)H_2(z_2)
, where
H_1(z_1)
and
H_2(z_2)
are stable, digital spectral transformations, originally proposed by Constantinides for a different purpose. This transformation is found to be analogous to McClellan's transformation for designing 2-D FIR filters like the circular, elliptic-support and fan filters. But the design of these filters, using our method, involves only a one-dimensional search procedure and not any optimization. The design procedure is very simple and guarantees stability of the resulting IIR filters at the same time. Design examples are included to illustrate the theory and also its relative simplicity.