Abstract
The discrete Gabor transform (DGT) is an important and widely used time–frequency analysis tool in signal processing. In this paper, a sparse time–frequency representation (TFR) method based on the DGT is studied using mixed \(\ell _{1/2}\)–\(\ell _2\) norm regularization which can overcome the over-sparse problem and permit a better sparsity and stability. Because the width of the window function in the DGT directly affects the time–frequency resolution and concentration of the Gabor spectrum, an adaptive optimal window width (AOWW) selection algorithm based on information entropy theory can be applied to search for the optimal width in the DGT. In this paper, the traditional DGT is converted into a constraint optimization problem by minimizing a mixed \(\ell _{1/2}\)–\(\ell _2\) norm sparse constraint of the Gabor coefficients. The numerical experimental results show that the proposed sparsity-based TFR based on the conventional DGT is an effective and powerful tool for analyzing and processing nonstationary signals, obtaining a higher time–frequency concentration and sparsity of the Gabor TFR of a given signal.
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Acknowledgements
The authors would like to express our sincere gratitude to the anonymous referees for their constructive comments. This work was supported in part by the National Natural Science Foundation of China under Grant No. 61301295, the Anhui Provincial Natural Science Foundation under Grant No. 1708085MF151, the Natural Science Foundation for the Higher Education Institutions of Anhui Province under Grant No. KJ2018A0018, and the Natural Science Foundation of Anhui Science and Technology University under Grant No. XWYJ201802.
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Li, R., Zhou, J. Sparse Gabor Time–Frequency Representation Based on \(\ell _{1/2}\)–\(\ell _2\) Regularization. Circuits Syst Signal Process 38, 4700–4722 (2019). https://doi.org/10.1007/s00034-019-01077-2
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DOI: https://doi.org/10.1007/s00034-019-01077-2