Design of Sparse FIR Filters With Joint Optimization of Sparsity and Filter Order

In this paper, two novel algorithms are developed to design sparse linear-phase (LP) FIR filters. Compared to traditional design methods, they can jointly optimize coefficient sparsity and order of an LP FIR filter, so as to achieve a balance between filtering performance and implementation efficien...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. I, Regular papers Vol. 62; no. 1; pp. 195 - 204
Main Authors: Jiang, Aimin, Kwan, Hon Keung, Zhu, Yanping, Liu, Xiaofeng, Xu, Ning, Tang, Yibin
Format: Journal Article
Language:English
Published: New York IEEE 01.01.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Balancing
Circuits
Design engineering
Equivalence
Filter order
Filtering
FIR filters
Heuristic
iterative-reweighted-least-squares (IRLS)
Least squares methods
linear phase
Minimization
Optimization
Quadratic programming
quadratic programming (QP)
sparse FIR filter
Sparse matrices
Sparsity
weighted l_{0} -norm minimization
ISSN:1549-8328, 1558-0806
Online Access:Get full text
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Summary:In this paper, two novel algorithms are developed to design sparse linear-phase (LP) FIR filters. Compared to traditional design methods, they can jointly optimize coefficient sparsity and order of an LP FIR filter, so as to achieve a balance between filtering performance and implementation efficiency. The design problem under consideration is formally cast as a regularized l 0 -norm minimization problem, which is then tackled by two different design algorithms. In the first proposed algorithm, the objective function of the original design problem is replaced by its upper bound, which leads to a weighted l 0 -norm minimization problem, while in the second one a group of auxiliary variables are introduced such that the original design problem can be equivalently transformed to another weighted l 0 -norm minimization problem. The iterative-reweighted-least-squares (IRLS) algorithm is employed with appropriate modifications to solve both weighted l 0 -norm minimization problems. Simulation results show that, compared to traditional approaches, the proposed algorithms can achieve comparable or better design results in terms of both sparsity and effective filter order.
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ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2014.2354771