Design of zero-phase spherically symmetric N-dimensional IIR digital filters

The authors present a new method for designing zero-phase N -dimensional IIR digital filters satisfying given amplitude design specifications. The method is based on applying the N-dimensional extension of McClellan transformation to the square of a one-dimensional IIR digital filter design recently proposed by Charalambous (1988). The resulting N-dimensional digital filter is of zero-phase and hyperspherically symmetric but unstable. Stabilisation of the filter is achieved by dividing it into a product of 2N filters, each of which is stable if realised through a recursion in the suitable quadrant. The stabilisation procedure uses the properties of the complex cepstrum. Three examples are introduced to show the performance and validity of the design method presented. The designs obtained are also tested in image processing applications