Fourier-Bessel Domain based Discrete Stockwell Transform for the Analysis of Non-stationary Signals

In this article, a novel time-frequency (TF) analysis approach based on the Fourier-Bessel series expansion (FBSE) domain discrete Stockwell transform (DST) is proposed. The Toeplitz matrix is formulated using the FBSE coefficients of the non-stationary signal. The Gaussian matrix is multiplied by the Toeplitz matrix to obtain the windowed Fourier-Bessel Toeplitz (WFBT) matrix. The FBSE-DST time-frequency representation (TFR) is evaluated based on inverse FBSE of WFBT matrix followed by Bessel function root to frequency transformation. The synthetic signals such as multicomponent damped sinusoidal, multicomponent based amplitude modulation (AM), multicomponent based frequency modulation (FM) signals, and real-time signals such as the electroencephalogram (EEG) signals are used to assess the performance of the proposed FBSE-DST approach. The Renyi-entropy measure is computed in each signal case to compare the performance of FBSE-DST and DST techniques. The results of the proposed FBSE-DST technique provide the Renyi entropy values of 15.90, 18.28, and 18.67, respectively, for the TFRs of multicomponent damped sinusoidal, multicomponent AM, multicomponent FM signals. The Renyi entropy values obtained using FBSE-DST are lower than that obtained by the DST approach for the TF analysis of different synthetic signals.