Design of separable denominator 2-dimensional digital filters possessing real circularly symmetric frequency responses

A new formulation of the approximation procedure to design 2-dimensional digital filters with separable denominators possessing real circularly symmetric frequency-response characteristics is described. In this scheme, a 1-dimensional function approximating the response on the axes of the 2-dimensional plane is first obtained. The 2-dimensional function is then constructed from the 1-dimensional function by adding extra terms, whose coefficients are determined employing an optimisation procedure, so as to yield the desired response, as closely as possible, in the rest of the 2-dimensional plane. Techniques to reduce the number of unknown coefficients to be determined by optimisation are also discussed.