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Introduction
The non-stationary signals have time varying statistical properties. The non-stationary signal processing has immense applications in diverse domains like biomedical signal analysis [1], speech signal processing [2], vibrational data interpretation [3], and financial data modeling [4]. The analysis of these non-stationary signals can be achieved by different methods based on time–frequency (T-F) analysis [5], decomposition methods [6], and wavelets [7].
A multi-component non-stationary signal consists of multiple mono- components whose spectral information varies with time. For spectral analysis of non-stationary signals, the study of the instantaneous frequency (IF) of mono components is important. Estimation of the IF of mono components can be done with the help of T–F analysis or by decomposition methods [8]. The T–F analysis projects a time series signal onto the T–F plane, where the variation of IF of the mono component can be observed. The Wigner–Ville distribution (WVD), wavelet transform (WT), and short-time Fourier transform (STFT) are some methods that exist for the analysis of non-stationary signals in the T–F plane [9, 10–11]. The STFT with a moving window concept implies the segment-wise Fourier transform results in a two-dimensional T–F distribution. However, the resolution of STFT-based T–F representation depends on window length [10, 12]. The WT offers the time-scale representation of the signal through the multi-resolution analysis [13]. The WT uses the translated and shifted wavelets in different time scales [14]. The WVD belongs to the Cohen class of distributions [1]. The WVD exhibits a quadratic nature and provides the best resolution in the T–F plane [1]. The main drawback of WVD in multi-component signals is the cross-terms in the T–F distribution [15]. The presence of cross-terms misleads the interpretation of mono components in the WVD-based T–F plane [16].
Some common signal decomposition methods are empirical mode decomposition (EMD), empirical WT (EWT), variational mode decomposition (VMD), ensemble EMD (EEMD), and tunable quality (Q) factor WT-based filter bank (TQFWT-FB) method [16, 17, 18, 19–20]. The EMD is proposed in [18], and the method is designed to decompose a signal into multiple intrinsic mode functions (IMFs). The input data went through an iterative process that extracts inherent oscillations using the signal extrema and their associated interpolation through a sifting process.
However, the limitation of the EMD method is the lack...