Two-dimensional digital filters with variable magnitude characteristics obtained from a 1-D monotonic response

A method for the generation of discreted domain two-dimensional (2-D) transfer functions possessing variable magnitude and contour characteristics is presented in this paper. The proposed method is based upon a configuration constituted by two 1-D filters in cascade and a feedback loop. Each of these 1-D filter is designed to have a monotonic magnitude frequency response. This is obtained by performing one or several integrations, either with respect to ω or ω², of the denominator of a magnitude Butterworth low-pass frequency response and obtaining the corresponding modified transfer function. The variable characteristics in each domain are obtained by changing a multiplier either in the forward path or in the feedback path of the proposed general configuration. The use of a generalized bilinear transformation (GBT) on the transfer functions obtained by the above mentioned method permits the generation of a large number of different characteristics. A certain number of these characteristics is examined in some detail. Illustrative examples are provided.