Realization structure for a class of 2D recursive digital filters with circular symmetric response

An efficient method is presented for the design of a class of 2-D recursive digital filters with separable denominators and non-separable numerator transfer functions. Two 1-D analog filters in s₁ and s₂ variables are designed to meet the specification along ω₁ and ω₂ axes using analog filter theory and then discretized by the application of a double bilinear transformation. The resulting 2-D filter has a rectangular cutoff boundary. This separable product 2-D filter is then cascaded by a 2-D FIR filter. Coefficients of this 2-D FIR filter can then be determined through minimization of an objective function so that the desired magnitude specification is obtained. This transfer function is realized using a least sensitive structure described in this work. An example is given to illustrate the usefulness of the proposed technique