Fourier-Bessel series expansion based empirical wavelet transform for analysis of non-stationary signals

In this paper, a new method has been presented for the time-frequency (TF) representation of non-stationary signals. The existing empirical wavelet transform (EWT) has been enhanced using Fourier-Bessel series expansion (FBSE) in order to obtain improved TF representation of non-stationary signals. We have used the FBSE method for the spectral representation of the analyzed multi-component signals with good frequency resolution. The scale-space based boundary detection method has been applied for the accurate estimation of boundary frequencies in the FBSE based spectrum of the signal. After that, wavelet based filter banks have been generated in order to decompose non-stationary multi-component signals into narrow-band components. Finally, the normalized Hilbert transform has been applied for the estimation of amplitude envelope and instantaneous frequency functions from the narrow-band components and obtained the TF representation of the analyzed non-stationary signal. We have applied our proposed method for the TF representation of multi-component synthetic signals and real electroencephalogram (EEG) signals. The proposed method has provided better TF representation as compared to existing EWT method and Hilbert-Huang transform (HHT) method, especially when analyzed signal possesses closed frequency components and of short time duration.