FIR filter design by iterative convex relaxations with rank refinement

Date
2014
Advisor
Instructor
Source Title
Proceedings of the 22nd Signal Processing and Communications Applications Conference, SIU 2014
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Electronic ISSN
Publisher
IEEE
Volume
Issue
Pages
654 - 657
Language
Turkish
Type
Conference Paper
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Volume Title
Abstract

Finite impulse response (FIR) filters have been a primary topic of digital signal processing since their inception. Although FIR filter design is an old problem, with the developments of fast convex solvers, convex modelling approach for FIR filter design has become an active research topic. In this work, we propose a new method based on convex programming for designing FIR filters with the desired frequency characteristics. FIR filter design problem, which is modelled as a non-convex quadratically constrained quadratic program (QCQP), is transformed to a semidefinite program (SDP). By relaxing the constraints, a convex programming problem, which we call RSDP(Relaxed Semidefinite Program), is obtained. Due to the relaxation, solution to the RSDPs fails to be rank-1. Typically used rank-1 approximations to the obtained RSDP solution does not satisfy the constraints. To overcome this issue, an iterative algorithm is proposed, which provides a sequence of solutions that converge to a rank-1 matrix. Conducted experiments and comparisons demonstrate that proposed method successfully designs FIR filters with highly flexible frequency characteristics.

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Book Title
Keywords
FIR filter, Quadratically constrained quadratic programming, Rank refinement, Semidefinite programming, Convex optimization, Convex programming, Filter banks, Iterative methods, Quadratic programming, Relaxation processes, Convex programming problems, Frequency characteristic, Semidefinite programs
Citation
Published Version (Please cite this version)