Design of circularly symmetric two-dimensional linear-phase low-pass FIR filters using closed-form expressions

A design technique is presented for two-dimensional linear phase low-pass FIR filters based on a constrained minimization formulation. The minimization criterion is a convex combination of two criteria representing measures of the error between the actual and ideal frequency responses in the pass and stop bands. The constraints can for example represent flatness conditions at the origin. The result is applied to the case of a circularly symmetric low-pass filter and closed-form expressions are derived for the elements of the relevant matrices which appear in the minimization criterion so that numerical integration can be avoided.