ABSTRACT

Equation (92.1) is the general form of transfer functions of the nonseparable numerator and denominator 2-D IIR filters. It can involve two subclasses, namely, the separable product transfer function

(92.6)

and the separable denominator, nonseparable numerator transfer function given by

(92.7)

The stability constraints for the above two transfer functions are the same as those for the individual two 1-D cases. These are easy to check and correspondingly the transfer function is easy to stabilize if the designed filter is found to be unstable. Therefore, in the design of the above two classes, in order to reduce the stability problem to that of the 1-D case, the denominator of the 2-D transfer function is chosen to have two 1-D polynomials in

z

and

z

variables in cascade. However, in the general formulation of nonseparable numerator and denominator filters, this oversimplification is removed. The filters of this type are generally designed either through transformation of 1-D filters, or through optimization approaches, as is discussed in the following.