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A Low Computational Complexity Scheme for Designing Linear Phase Sparse FIR Filters

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Abstract

A low complexity scheme is developed to design the sparse linear phase FIR filters based on the improved iteratively re-weighted orthogonal matching pursuit(OMP) algorithm. The scheme employs the Frobenius norm to simplify searching for the desired sparse FIR filter at each iteration. Furthermore, a log function is introduced to enhance the weight updating process at each iteration. The simulation results demonstrate that our scheme can effectively generate the sparse linear phase FIR filters which satisfy the various given design specifications.

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Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 61771262).

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Authors and Affiliations

  1. College of Electronic Information and Optical Engineering, Nankai University, Tianjin, China

    Yi Li, Jiaxiang Zhao & Guiling Sun

  2. School of Electronics and Information Engineering, Tianjin Polytechnic University, Tianjin, China

    Wei Xu

Authors
  1. Yi Li
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  2. Jiaxiang Zhao
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  3. Wei Xu
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  4. Guiling Sun
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Contributions

All authors contributed to the study conception and design. Material preparation, derivation of formula, Programming and analysis were performed by Yi Li, Jiaxiang Zhao, Wei Xu and Guiling Sun. The first draft of the manuscript was written by Yi Li and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Jiaxiang Zhao.

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Appendix

Appendix

See Tables 10, 11, 12 and 13.

Table 10 Nonzero taps of sparse FIR low pass filter (with \(N=80\) and \(\delta _s=-20\) dB) generated by proposed algorithm in Example 1
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Table 11 Nonzero taps of sparse FIR low pass filter (\(\omega _p=0.4\pi \) and \(\eta =0.1\pi \)) generated by proposed algorithm in Example 2
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Table 12 Nonzero taps of sparse FIR low pass filter (\(\omega _p=0.45\pi \) and \(\eta =0.11\pi \)) generated by proposed algorithm in Example 2
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Table 13 Nonzero taps of sparse FIR low pass filter (\(N=180\) and \(\delta _s<-70\) dB) generated by proposed algorithm in Example 3
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Li, Y., Zhao, J., Xu, W. et al. A Low Computational Complexity Scheme for Designing Linear Phase Sparse FIR Filters. Circuits Syst Signal Process 41, 1550–1562 (2022). https://doi.org/10.1007/s00034-021-01836-0

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  • DOI: https://doi.org/10.1007/s00034-021-01836-0

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