Design of nearly linear-phase recursive digital filters by constrained optimization

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dc.contributor.author Guindon, David Leo
dc.date.accessioned 2007-12-24T22:31:42Z
dc.date.available 2007-12-24T22:31:42Z
dc.date.copyright 2007 en_US
dc.date.issued 2007-12-24T22:31:42Z
dc.identifier.uri http://hdl.handle.net/1828/296
dc.description.abstract The design of nearly linear-phase recursive digital filters using constrained optimization is investigated. The design technique proposed is expected to be useful in applications where both magnitude and phase response specifications need to be satisfied. The overall constrained optimization method is formulated as a quadratic programming problem based on Newton’s method. The objective function, its gradient vector and Hessian matrix as well as a set of linear constraints are derived. In this analysis, the independent variables are assumed to be the transfer function coefficients. The filter stability issue and convergence efficiency, as well as a ‘real axis attraction’ problem are solved by integrating the corresponding bounds into the linear constraints of the optimization method. Also, two initialization techniques for providing efficient starting points for the optimization are investigated and the relation between the zero and pole positions and the group delay are examined. Based on these ideas, a new objective function is formulated in terms of the zeros and poles of the transfer function expressed in polar form and integrated into the optimization process. The coefficient-based and polar-based objective functions are tested and compared and it is shown that designs using the polar-based objective function produce improved results. Finally, several other modern methods for the design of nearly linear-phase recursive filters are compared with the proposed method. These include an elliptic design combined with an optimal equalization technique that uses a prescribed group delay, an optimal design method with robust stability using conic-quadratic-programming updates, and an unconstrained optimization technique that uses parameterization to guarantee filter stability. It was found that the proposed method generates similar or improved results in all comparative examples suggesting that the new method is an attractive alternative for linear-phase recursive filters of orders up to about 30. en_US
dc.language English eng
dc.language.iso en en_US
dc.rights Available to the World Wide Web en_US
dc.subject optimization en_US
dc.subject digital filter en_US
dc.subject constrained optimization en_US
dc.subject recursive digital filter en_US
dc.subject linear-phase en_US
dc.subject IIR en_US
dc.subject quadratic programming en_US
dc.subject filter stability en_US
dc.subject gradient en_US
dc.subject hessian en_US
dc.subject equalizer en_US
dc.subject.lcsh UVic Subject Index::Sciences and Engineering::Engineering::Electrical engineering en_US
dc.title Design of nearly linear-phase recursive digital filters by constrained optimization en_US
dc.type Thesis en_US
dc.contributor.supervisor Antoniou, Andreas
dc.contributor.supervisor Shpak, Dale J.
dc.degree.department Dept. of Electrical and Computer Engineering en_US
dc.degree.level Master of Applied Science M.A.Sc. en_US

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