Analytical design of multidimensional recursive digital filters with cubic symmetry and constant group delays

An analytical technique is developed for designing multidimensional (M-D) separable-denominator recursive digital filters that meet, simultaneously, magnitude and phase specifications. A cubic symmetry that exists in the M-D frequency response is incorporated into the M-D filter structure. The denominator and the numerator of an M-D transfer function are designed separately. The former is used to approximate constant group delays and the latter is used to adjust an overall magnitude response. The filter is analytically designed by solving linear equations only. This serves to reduce the amount of calculations drastically. The stability of the resulting filter is always guaranteed. Finally an example is given to illustrate the utility of the proposed technique.