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

Abstract

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.

On single row routing

“…where 7 = 0 or 1, Lisa positive integer such that J + 2L = 2M < N. The unknowns a,-, £,(/ = 1,2,-• •, L) of (14) can be determined by a nonlinear optimization algorithm such as the Fletcher-Powell algorithm [13] when combined with either (8) or (9) to meet a given set of magnitude and linear phase specifications. This provides an alternative approach to the design of the 2-D non-recursive filter.…”

“…It is well known, that 2-D zero-input recursive filters can also exhibit periodic limit cycles. Criteria for the absence of (separable) periodic sequences were obtained in [7], [8]. Periodic limit cycles in 2-D digital filters have also been studied in [9], [10].…”