Multidimensional spherically symmetric recursive digital filter design satisfying prescribed magnitude and constant group delay responses

A computationally efficient technique for the design of multidimensional spherically symmetric recursive digital filters satisfying prescribed magnitude and constant group delay specifications is presented. The denominator and the numerator of the transfer function are designed separately. The former is used to approximate the group delay response and the latter is used to approximate the magnitude response. Moreover, this method also makes use of the symmetric conditions of the transfer function. Therefore the numbers of parameters and sample points required for the optimisation are greatly reduced. As a result, the amount of computation can be minimised and the convergence can also be improved. Such advantages are extremely significant for high order multidimensional filter design. Two examples of the 2-dimensional and one example of the 3-dimensional digital filter design are given to illustrate the proposed method. Comparisons with the results of other methods are also given.