A new 2-D zero phase digital filter design with quadrantally symmetric or antisymmetric properties

A closed-form least-squares solution for the problem of designing two-dimensional (2-D) real zero phase Finite Impulse Response (FIR) filters with quadrantally symmetric or antisymmetric properties is obtained. Then a 2-D Infinite Impulse Response (IIR) filter is synthesized as an approximation of the designed 2-dimensional FIR filter by using the decomposition theorem and the 1-D balanced approximation (BA) method. The designed 2-D IIR filter retains good zero phase property over the passband region. The magnitude error between the 2-D FIR and the 2-D IIR filter is small and can be obtained from the BA method