Complex-valued Thiran allpole filters

Authors:
Alfonso Fernandez-Vazquez;Gordana Jovanovic Dolecek
Affiliations:
School of Computer Engineering/ ESCOM, National Polytechnic Institute/ IPN, Mexico City, 07738, Mexico;Department of Electronics, National Institute of Astrophysics, Optics, and Electronics/ INAOE, Puebla, 72840, Mexico
Venue:
Digital Signal Processing
Year:
2013

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Abstract

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 @f"@a, the group delay @t, and the degree of flatness K at @w=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 @t and @f"@a. Finally, the application of the proposed filters for the design of a casual complex-valued cardinal orthogonal scaling function is described.