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A Class of Deterministic Sensing Matrices and Their Application in Harmonic Detection

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Abstract

In this paper, a class of deterministic sensing matrices are constructed by selecting rows from Fourier matrices. These matrices have better performance in sparse recovery than random partial Fourier matrices. The coherence and restricted isometry property of these matrices are given to evaluate their capacity as compressive sensing matrices. In general, compressed sensing requires random sampling in data acquisition, which is difficult to implement in hardware. By using these sensing matrices in harmonic detection, a deterministic sampling method is provided. The frequencies and amplitudes of the harmonic components are estimated from under-sampled data. The simulations show that this under-sampled method is feasible and valid in noisy environments.

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Notes

  1. When N is a prime number and \(N \,\hbox { mod }\,4=1\), the corresponding matrices have worse sensing properties than the proposed matrices.

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Authors and Affiliations

  1. Signal Processing Lab, School of Electronic Information, Wuhan University, Wuhan, 430072, China

    Shan Huang, Hong Sun, Lei Yu & Haijian Zhang

Authors
  1. Shan Huang
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  2. Hong Sun
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  3. Lei Yu
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  4. Haijian Zhang
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Corresponding author

Correspondence to Haijian Zhang.

Additional information

This work was supported in part by the National Natural Science Foundation of China under Grant No. 61501335 and in part by the Natural Science Foundation of Hubei Province (No. 2015CFB202).

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Huang, S., Sun, H., Yu, L. et al. A Class of Deterministic Sensing Matrices and Their Application in Harmonic Detection. Circuits Syst Signal Process 35, 4183–4194 (2016). https://doi.org/10.1007/s00034-016-0245-3

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  • DOI: https://doi.org/10.1007/s00034-016-0245-3

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