Approximation of two‐dimensional digital filters by separable‐denominator rational function

Abstract

An efficient procedure is presented for obtaining a rational function having separable denominator from a given twodimensional (2‐D) impulse response over the first quadrant. First, it is shown that the class of rational functions with separable denominator can be characterized by two 1‐D systems and the given 2‐D impulse response is expressed formally in terms of those of two 1‐D systems. Next, a 1‐D rational approximation is done to each of the impulse responses of two formally 1‐D systems using first‐ and second‐order data from it and the coefficients in the numerator of 2‐D rational function are calculated such that the impulse response of the approximating 2‐D rational function coincides with the given one around the origin. Finally, it is proved that the BIBO stability of the approximating filters is always ensured for given BIBO‐stable 2‐D impulse responses.