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An Extrapolated Impulse Response Filter Design with Sparse Coefficients Based on a Novel Linear Approximation of Matrix

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Abstract

A novel method of linear approximation of a matrix is proposed for designing the linear-phase and non-linear-phase extrapolated impulse response (EIR) filters. There are zero-valued and one-valued coefficients in the scale vectors of the proposed EIR filters. These zero-valued coefficients do not require multipliers or adders, and these one-valued coefficients do not require multipliers, in the filter implementation. Additionally, the optimal design of the EIR filters in the mini-max sense and the least-square sense by the iterative gradient searching (IGS) technique is investigated. In implementing the IGS technique, the original EIR filter, the principal component analysis based EIR filter and the proposed EIR filter are set as the initial solutions, separately. If the proposed EIR filter is set as the initial solution, the IGS technique can synthesize the prototype finite impulse response (FIR) filter satisfactorily, with the lowest hardware implementation complexity. Further, experimental comparison of the proposed EIR method with the two most popular non-EIR low-complexity FIR filter design methods also indicates some superiority of the proposed EIR method. Finally, the proposed method of linear approximation of a matrix may also be useful in other areas of signal processing.

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Acknowledgments

The authors would like to thank the anonymous referees and Haixian Wang for constructive recommendations.This work was supported by the Natural Science Foundation of ZhejiangProvince under Grants Nos. LY12F01006 and LY14F010010, the Scientific Research Foundation of Department of Education of Zhejiang Province under Grants No. Y201329723, and the Natural Science Foundation of China under Grant Nos. 61375028, 61273266 and 61301219.

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Authors and Affiliations

  1. School of Communication Engineering, Hangzhou Dianzi University, Hangzhou, 310018, Zhejiang, People’s Republic of China

    Hao Wang

  2. School of Information Science and Engineering, Southeast University, Nanjing, 210096, Jiangsu, People’s Republic of China

    Hao Wang

  3. School of Information Engineering, Huzhou Teachers’ College, Huzhou, 313000, Zhejiang, People’s Republic of China

    Xinmin Cheng & Wenjun Hu

  4. School of Information Science and Engineering, Southeast University, Room 204, Jianxiong Building, Nanjing, 210096, Jiangsu, People’s Republic of China

    Peng Song & Ling Yu

  5. School of Information Science and Engineering, Southeast University, Room 313, Jianxiong Building, Nanjing, 210096, Jiangsu, People’s Republic of China

    Li Zhao

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  1. Hao Wang
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  2. Xinmin Cheng
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  3. Peng Song
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  4. Ling Yu
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  5. Wenjun Hu
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  6. Li Zhao
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Correspondence to Hao Wang.

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Wang, H., Cheng, X., Song, P. et al. An Extrapolated Impulse Response Filter Design with Sparse Coefficients Based on a Novel Linear Approximation of Matrix. Circuits Syst Signal Process 34, 2335–2361 (2015). https://doi.org/10.1007/s00034-014-9955-6

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  • DOI: https://doi.org/10.1007/s00034-014-9955-6

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