Optimal Design of Notch Filter with Principal Basic Vectors in Subspace

Jinguang HAO; Gang WANG; Lili WANG; Honggang WANG

doi:10.1587/transfun.E101.A.723

Optimal Design of Notch Filter with Principal Basic Vectors in Subspace

Jinguang HAO, Gang WANG, Lili WANG, Honggang WANG

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Summary :

In this paper, an optimal method is proposed to design sparse-coefficient notch filters with principal basic vectors in the column space of a matrix constituted with frequency samples. The proposed scheme can perform in two stages. At the first stage, the principal vectors can be determined in the least-squares sense. At the second stage, with some components of the principal vectors, the notch filter design is formulated as a linear optimization problem according to the desired specifications. Optimal results can form sparse coefficients of the notch filter by solving the linear optimization problem. The simulation results show that the proposed scheme can achieve better performance in designing a sparse-coefficient notch filter of small order compared with other methods such as the equiripple method, the orthogonal matching pursuit based scheme and the L₁-norm based method.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.4 pp.723-726

Publication Date: 2018/04/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E101.A.723

Type of Manuscript: LETTER

Category: Digital Signal Processing

Authors

Jinguang HAO
  Ludong University
Gang WANG
  Ludong University
Lili WANG
  Ludong University
Honggang WANG
  Ludong University

Keyword

notch filter, principal basic vectors, linear optimization, sparsity

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Jinguang HAO, Gang WANG, Lili WANG, Honggang WANG, "Optimal Design of Notch Filter with Principal Basic Vectors in Subspace" in IEICE TRANSACTIONS on Fundamentals, vol. E101-A, no. 4, pp. 723-726, April 2018, doi: 10.1587/transfun.E101.A.723.
Abstract: In this paper, an optimal method is proposed to design sparse-coefficient notch filters with principal basic vectors in the column space of a matrix constituted with frequency samples. The proposed scheme can perform in two stages. At the first stage, the principal vectors can be determined in the least-squares sense. At the second stage, with some components of the principal vectors, the notch filter design is formulated as a linear optimization problem according to the desired specifications. Optimal results can form sparse coefficients of the notch filter by solving the linear optimization problem. The simulation results show that the proposed scheme can achieve better performance in designing a sparse-coefficient notch filter of small order compared with other methods such as the equiripple method, the orthogonal matching pursuit based scheme and the L₁-norm based method.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.723/_p

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@ARTICLE{e101-a_4_723,
author={Jinguang HAO, Gang WANG, Lili WANG, Honggang WANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Optimal Design of Notch Filter with Principal Basic Vectors in Subspace},
year={2018},
volume={E101-A},
number={4},
pages={723-726},
abstract={In this paper, an optimal method is proposed to design sparse-coefficient notch filters with principal basic vectors in the column space of a matrix constituted with frequency samples. The proposed scheme can perform in two stages. At the first stage, the principal vectors can be determined in the least-squares sense. At the second stage, with some components of the principal vectors, the notch filter design is formulated as a linear optimization problem according to the desired specifications. Optimal results can form sparse coefficients of the notch filter by solving the linear optimization problem. The simulation results show that the proposed scheme can achieve better performance in designing a sparse-coefficient notch filter of small order compared with other methods such as the equiripple method, the orthogonal matching pursuit based scheme and the L₁-norm based method.},
keywords={},
doi={10.1587/transfun.E101.A.723},
ISSN={1745-1337},
month={April},}

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TY - JOUR
TI - Optimal Design of Notch Filter with Principal Basic Vectors in Subspace
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 723
EP - 726
AU - Jinguang HAO
AU - Gang WANG
AU - Lili WANG
AU - Honggang WANG
PY - 2018
DO - 10.1587/transfun.E101.A.723
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2018
AB - In this paper, an optimal method is proposed to design sparse-coefficient notch filters with principal basic vectors in the column space of a matrix constituted with frequency samples. The proposed scheme can perform in two stages. At the first stage, the principal vectors can be determined in the least-squares sense. At the second stage, with some components of the principal vectors, the notch filter design is formulated as a linear optimization problem according to the desired specifications. Optimal results can form sparse coefficients of the notch filter by solving the linear optimization problem. The simulation results show that the proposed scheme can achieve better performance in designing a sparse-coefficient notch filter of small order compared with other methods such as the equiripple method, the orthogonal matching pursuit based scheme and the L₁-norm based method.
ER -