Design of two-dimensional digital filters via spectral transformations

Complex maps, with domains and codomains consisting of rational transfer functions, have often been used in designing two-dimensional (2-D) digital filters. Such maps, commonly known as spectral transformations, have the important property of carrying a stable rational transfer function to another stable rational function. This paper presents a unified framework for designing 2-D stable digital filters from prescribed magnitude-response specifications using spectral transformations such that the magnitude response of the resultant approximation is sort of a "best" approximation of the given specification. It is shown that there are two basic strategies for such designs, each with its own advantages and disadvantages. The design procedures are illustrated with practical examples. Further, it is also shown that all earlier results on 2-D filter design using spectral transformations follow as special cases of the general theory presented here.