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Improved Eigenvalue Decomposition-Based Approach for Reducing Cross-Terms in Wigner–Ville Distribution

A Correction to this article was published on 06 June 2018

This article has been updated


In this work, a novel data-driven methodology is proposed to reduce cross-terms in the Wigner–Ville distribution (WVD) using improved eigenvalue decomposition of the Hankel matrix (IEVDHM). The IEVDHM method decomposes a multi-component non-stationary (NS) signal into mono-component NS signals. After that, amplitude-based segmentation is applied to obtain the components which are separated in time domain. Further, frequency modulation (FM) rate of components is observed to achieve an adaptive window. The adaptive window successfully removes intra-cross-terms which are generated due to nonlinearity present in FM. Finally, the sum of WVD of all the components is considered the WVD of the multi-component NS signal. The simulation study has been carried out on synthetic and natural signals to show the effectiveness of the proposed method. Performance of the proposed method is compared with the existing methods. We have also evaluated the performance of the proposed method in additive white Gaussian noise environment. The normalized Renyi entropy measure is computed to show the efficacy of the proposed method and all the compared methods for obtaining time–frequency representation.

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Change history

  • 06 June 2018

    The original version of the article unfortunately contained few errors in reference citations and equations. This has been corrected with this erratum.


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Sharma, R.R., Pachori, R.B. Improved Eigenvalue Decomposition-Based Approach for Reducing Cross-Terms in Wigner–Ville Distribution. Circuits Syst Signal Process 37, 3330–3350 (2018).

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  • Eigenvalue decomposition
  • Hankel matrix
  • Wigner–Ville distribution
  • Cross-terms
  • Time–frequency representation