Design of multidimensional recursive digital filters using the composite property mapping algorithm

A systematic frequency domain design approach is presented for designing multidimensional recursive digital filters that approximate prescribed ideal frequency response specifications. The composite property mapping algorithm is used to generate a frequency response matrix which possesses properties associated with a recursive filter. This design procedure results in a filter transfer function whose associated frequency response closely approximates the ideal filter's magnitude and phase specifications. To illustrate the proposed method, two- and three-dimensional filters are synthesized and compared with existing techniques. The results demonstrate that the recursive digital filters designed by the proposed approach have significantly reduced the relative root mean square errors compared with the conventional methods and have the required zero phase response.