Generation of a class of two-dimensional (2-D) transfer functions yielding variable magnitude and contour characteristics

The properties of a two-dimensional (2-D) discrete transfer function with the degree of each variable being unity are discussed. The coefficients of the denominator polynomial contain a parameter k (having real values) whose bounds are determined by stability considerations. These bounds are obtained by testing the overall polynomial at only four points z/sub 1/=/spl plusmn/1 and z/sub 2/=/spl plusmn/1. A suitable numerator polynomial can be associated to get the overall transfer function. By varying the values of k, different magnitude and contour characteristics are obtained. Such structures can be cascaded so that the magnitude responses can be varied.