Design of Novel Time-Frequency Tool for Non-stationary α-Stable Environment and its Application in EEG Epileptic Classification

Fractional lower-order time-frequency distributions (FLO-TFDs) exhibit all the advantages of established time-frequency (TF) tools and offer robustness for even non-Gaussian noise environments. Therefore, this paper presents a novel extension to the existing FLO-TFDs known as fractional lower-order fractional Stockwell transform (FLO-FrST), with the aim of enhancing resolution, reconstruction and robustness. The proposed tool is analytically designed by amalgamating the advantages of fractional Fourier transform (FrFT), Stockwell transform (ST) and fractional lower-order statistics (FLOS). To demonstrate the efficacy of the suggested FLO-FrST tool, an experimental study is demonstrated, which includes a comparison with established methodologies in terms of qualitative and quantitative analysis using performance metric parameters; Jones-Park (JP) measure and root-mean-square error (RMSE). The high value of JP measure and the low value of RMSE obtained establish the superiority of the proposed tool. Finally, an application of using this tool as a 2-dimensional (2-D) mapping tool is illustrated in electroencephalogram (EEG) epileptic classification using a deep learning approach. The proposed classification methodology is validated and compared with established TF and FLO-TF methods in terms of sensitivity, positive predictivity, accuracy, error rate, F1-score and Matthew's correlation coefficient. The overall performance of the proposed tool presented in current study showcases its precedence over state-of-the-art methods, indicating its potential as a tool for achieving high-resolution and improved reconstruction in both non-Gaussian alpha\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha$$\end{document}-stable and Gaussian environments.