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A Sparse Analysis Window for Discrete Gabor Transform

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Abstract

Here, we analyze sparse analysis windows for complex-valued and real-valued discrete Gabor transforms. A number of theories presented in this study indicate that the existence and uniqueness of a sparse analysis window for a given synthesis window depend to a great extent on the sparsity of the synthesis window. Specifically, the upper and lower bounds on the analysis window sparsity are obtained for synthesis windows of different sparsities and analyzed in detail. Particularly, if the sparsity of a given synthesis window with connected support is equal to the discrete Gabor transform time-shift parameter, the sparsest analysis window is unique. In addition, we propose an algorithm that searches for a sparse analysis window. Compared with existing algorithms, a sparse analysis window with fewer nonzero elements and/or smaller reconstruction errors can be obtained with the proposed algorithm. A sequence of experimental results reveals its superior effectiveness. In addition, a better Gabor representation with high concentration and time–frequency resolution is obtained with the sparse analysis window.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61301295 and 61372137, the Natural Science Foundation of Anhui Province under Grant No. 1708085MF151 and the Doctoral Fund of Anhui University. The authors would like to thank the anonymous reviewers for valuable input.

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Authors and Affiliations

  1. Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, Anhui University, Hefei, China

    Jian Zhou & Liang Tao

  2. Institute of Media Computing, Anhui University, Hefei, China

    Jian Zhou & Xianyong Fang

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  1. Jian Zhou
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  2. Xianyong Fang
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  3. Liang Tao
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Correspondence to Jian Zhou.

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Zhou, J., Fang, X. & Tao, L. A Sparse Analysis Window for Discrete Gabor Transform. Circuits Syst Signal Process 36, 4161–4180 (2017). https://doi.org/10.1007/s00034-017-0510-0

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