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Sliding Mode Singular Spectrum Analysis for the Elimination of Cross-Terms in Wigner–Ville Distribution


The Wigner–Ville distribution (WVD) is a signal processing approach to evaluate a high-resolution time–frequency representation (TFR) of a multi-component signal. The WVD of a multi-component signal produces unwanted cross-terms in the TFR. The elimination of these cross-terms using various signal processing techniques is a challenging research problem. In this paper, a data-driven signal decomposition technique is investigated for the elimination of these cross-terms in the WVD-based time–frequency representation of a multi-component signal. The approach is based on the decomposition of a multicomponent signal into its mono-components using sliding mode singular spectrum analysis (SM-SSA). The WVD of each mono-component is evaluated, and the sum of WVDs of all mono-components represents the cross-term free WVD representation of multi-component signals. Renyi entropy (RE) is used to quantify the performance of the proposed approach. Simulations are carried out using synthetic and real signals to verify the effectiveness of the proposed approach for the removal of cross-terms in WVD. The results demonstrated that SM-SSA has better performance with the lowest RE value as compared to other data-driven signal decomposition approaches such as automated SSA (AutoSSA) and swarm decomposition for the elimination of cross-terms from the WVD-based TFR of multi-component signals.

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Data Availability Statement

The signal files and the codes of the proposed work are available upon request to the authors.


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Funding was provided by Birla Institute of Technology and Science, Pilani (Grant No. FR/SCM/150618/EEE).

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Correspondence to R. K. Tripathy.

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Panda, R., Jain, S., Tripathy, R.K. et al. Sliding Mode Singular Spectrum Analysis for the Elimination of Cross-Terms in Wigner–Ville Distribution. Circuits Syst Signal Process 40, 1207–1232 (2021).

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  • Wigner–Ville distribution
  • Cross-terms
  • Sliding mode singular spectrum analysis
  • Time–frequency representation
  • Renyi entropy