Design methodology for nearly linear-phase recursive digital filters by constrained optimization

Authors:
David Guindon;Dale J. Shpak;Andreas Antoniou
Affiliations:
Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC, Canada;Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC, Canada;Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC, Canada
Venue:
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Year:
2010

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Abstract

A methodology for the design of recursive digital filters having nearly linear phase response is proposed. The underlying design method is of the direct type whereby the filter is designed as a single unit. The design problem is formulated as a cascade of filter sections where each section is represented by a biquadratic transfer function either in the conventional polynomial form or in the polar form. The design problem is then solved using a constrained Newton's method whereby constraints are used to assure the stability of the filter, to control the step size in order to achieve fast convergence, and to eliminate a real-axis pole-migration problem that often interferes with the design process. Several design examples demonstrate that when compared with filters designed using existing state-of-the-art methods, the proposed methodology yields filters having reduced order and/or improved performance.