FBSE-EWT Technique-based Complex-valued Signal Analysis

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. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.