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 ϕα, the group delay τ, and the degree of flatness K at ω=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 τ and ϕα. Finally, the application of the proposed filters for the design of a casual complex-valued cardinal orthogonal scaling function is described.