DESIGN OF STABLE 2-DIMENSIONAL ANALOG AND DIGITAL-FILTERS WITH APPLICATIONS IN IMAGE-PROCESSING

A method is proposed for the frequency domain design of linear two‐dimensional analogue and digital filters with guaranteed stability. The technique used is based on the result that the numerator and the denominator of the input immittance of a two‐variable network (which is passive and lossy) are strictly Hurwitz polynomials. One of these strictly Hurwitz polynomials is assigned to the denominator of a two‐variable analogue transfer function and the network elements are then used as the variables of optimization thereby guaranteeing the stability of the analogue transfer function. The transfer function of the corresponding two‐dimensional discrete (digital) filter is obtained from the analogue transfer function by the bilinear transformation. Examples illustrating the versatility of the technique in designing 2D digital filters of arbitrary order approximating a given magnitude and group delay response are presented. These filters are used to process a simple binary image. The results obtained demonstrate the importance of linear phase in image processing applications. The method presented here can be extended to the design of stable m‐dimensional analogue and digital filters. Copyright © 1979 John Wiley & Sons, Ltd.