Optimal Design of Notch Filter with Principal Basic Vectors in Subspace

Jinguang HAO  Gang WANG  Lili WANG  Honggang WANG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.4   pp.723-726
Publication Date: 2018/04/01
Online ISSN: 1745-1337
Type of Manuscript: LETTER
Category: Digital Signal Processing
Keyword: 
notch filter,  principal basic vectors,  linear optimization,  sparsity,  

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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.