Design of inherently stable two-dimensional recursive filters from one-dimensional filters

A novel method is described for the design of two-dimensional filters from one-dimensional filters while preserving stability. The proposed approach has several advantages when compared to other known transformation techniques. Because the numerator and the denominator are transformed independently, more free parameters are available to approximate a desired filter response. A relation between the coefficients of a digital one-dimensional prototype filter and the corresponding two-dimensional digital filter after the transformation as a function of a number of unconstrained free parameters is derived. This enables the optimization of a two-dimensional filter response to be carried out directly in the discrete domain.