Design of 2-D recursive digital filters with constant group delay characteristics using separable denominator transfer function and a new stability test

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

“…Samples can be chosen only on the w t axis in the range 0 < w t < n. Supposing that M' samples are chosen a t w i 9 5 9 = 1> 2, ..., M' and the corresponding group delays are i(w lfl ). The statement of the problem is to find the parameter vector b = 1, 2; k = 1, 2, ..., (15) so as to minimise the group delay performance index J(b) which is defined as M' 9 = 1 (16) where <r is the desired constant group delay, which is chosen to be a positive value [11], and u g is a non-negative weighting function and is equal to zero outside the passband. The Fletcher-Powell algorithm [17] is used in the optimisation of eqn.…”

“…However, to use a linear stability constraint, which is only a sufficient condition for stability, the method only yields a subclass of possible solutions. Besides, there are also some methods [10,11] which tackle this problem by choosing a performance index expressed as a linear combination of three error functions, i.e. one for the magnitude response and two for the group delay responses.…”