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FBSE-EWT Technique-based Complex-valued Signal Analysis

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Abstract

In this paper, we have proposed complex Fourier–Bessel series expansion-based empirical wavelet transform (CFBSE-EWT) and Hilbert spectral analysis (HSA) for time-frequency analysis of complex-valued signals. The proposed method obtains the real-valued positive and negative frequency components of the complex-valued signal using a suitable filter. Further, the obtained real-valued components are decomposed into corresponding set of subband signals using the Fourier–Bessel series expansion-based empirical wavelet transform (FBSE-EWT) method. The HSA is applied on the subband signals to obtain the time-frequency distribution (TFD). The effectiveness of the proposed CFBSE-EWT has been evaluated on two synthetic multicomponent complex-valued signals and a real-life wind signal. The decomposition results of CFBSE-EWT method are also compared with complex empirical mode decomposition (CEMD), complex flexible analytic wavelet transform (CFAWT), complex variational mode decomposition (CVMD), and complex improved eigenvalue decomposition of Hankel matrix (CIEVDHM) using the quality of reconstruction factor as performance objective measure. Additionally, the TFD of the synthetic complex-valued signals and real-life complex-valued wind signal is obtained from the proposed CFBSE-EWT-based HSA and compared with the CEMD-based HSA, CFAWT-based HSA, CVMD-based HSA, and CIEVDHM-based HSA methods. The CFBSE-EWT-based HSA provides improved TFD and it is useful for analysis of real-life complex-valued signals.

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Data Availability

The mathematical expression for the synthetic signals used for analysis has been given in the manuscript. Further, the data availability link of the real-time wind data used for analysis is also given in the reference.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota, Twin Cities, USA

    Aahan Tyagi

  2. Department of Electrical Engineering, Indian Institute of Technology Indore, Indore, India

    Vivek Kumar Singh & Ram Bilas Pachori

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  1. Aahan Tyagi
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  2. Vivek Kumar Singh
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  3. Ram Bilas Pachori
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Correspondence to Ram Bilas Pachori.

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Tyagi, A., Singh, V.K. & Pachori, R.B. FBSE-EWT Technique-based Complex-valued Signal Analysis. Circuits Syst Signal Process 44, 1349–1370 (2025). https://doi.org/10.1007/s00034-024-02887-9

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