FIR filter design by convex optimization using directed iterative rank refinement algorithm

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buir.contributor.authorArıkan, Orhan
buir.contributor.orcidArıkan, Orhan|0000-0002-3698-8888
dc.citation.epage2219en_US
dc.citation.issueNumber9en_US
dc.citation.spage2209en_US
dc.citation.volumeNumber64en_US
dc.contributor.authorDedeoğlu, M.en_US
dc.contributor.authorAlp, Y. K.en_US
dc.contributor.authorArıkan, Orhanen_US
dc.date.accessioned2018-04-12T10:42:21Z
dc.date.available2018-04-12T10:42:21Z
dc.date.issued2016en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractThe advances in convex optimization techniques have offered new formulations of design with improved control over the performance of FIR filters. By using lifting techniques, the design of a length-L FIR filter can be formulated as a convex semidefinite program (SDP) in terms of an L× L matrix that must be rank-1. Although this formulation provides means for introducing highly flexible design constraints on the magnitude and phase responses of the filter, convex solvers implementing interior point methods almost never provide a rank-1 solution matrix. To obtain a rank-1 solution, we propose a novel Directed Iterative Rank Refinement (DIRR) algorithm, where at each iteration a matrix is obtained by solving a convex optimization problem. The semidefinite cost function of that convex optimization problem favors a solution matrix whose dominant singular vector is on a direction determined in the previous iterations. Analytically it is shown that the DIRR iterations provide monotonic improvement, and the global optimum is a fixed point of the iterations. Over a set of design examples it is illustrated that the DIRR requires only a few iterations to converge to an approximately rank-1 solution matrix. The effectiveness of the proposed method and its flexibility are also demonstrated for the cases where in addition to the magnitude constraints, the constraints on the phase and group delay of filter are placed on the designed filter.en_US
dc.identifier.doi10.1109/TSP.2016.2515062en_US
dc.identifier.issn1053-587X
dc.identifier.urihttp://hdl.handle.net/11693/36497
dc.language.isoEnglishen_US
dc.publisherInstitute of Electrical and Electronics Engineers Inc.en_US
dc.relation.isversionofhttp://dx.doi.org/10.1109/TSP.2016.2515062en_US
dc.source.titleIEEE Transactions on Signal Processingen_US
dc.subjectConvex optimizationen_US
dc.subjectFinite impulse response (FIR) filter designen_US
dc.subjectIterative rank refinementen_US
dc.subjectSemidefinite programmingen_US
dc.subjectSemidefinite relaxationen_US
dc.subjectSpectral masken_US
dc.titleFIR filter design by convex optimization using directed iterative rank refinement algorithmen_US
dc.typeArticleen_US
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