Complex-valued Thiran allpole filters
This paper describes the generalization of the real-valued Thiran allpole filter to the complex case. The design specifications for the complex case are the phase value ?? ? ? , the group delay ?, and the degree of flatness K  at ?=0 ? = 0 . The complex filter coefficients are obtained by solving a set of closed form linear equations derived from the design specification. Depending on the parity of the degree of flatness K, we proposed three classes of complex-valued allpole filters. We also establish the stability conditions, which depend on ?  and ?? ? ? . Finally, the application of the proposed filters for the design of a casual complex-valued cardinal orthogonal scaling function is described.
allpole filter complex iir filter maximally flat thiran filter