Time–frequency representation (TFR) is useful for non‐stationary signal analysis as it provides information about the time‐varying frequency components. This study proposes a novel TFR based on the improved eigenvalue decomposition of Hankel matrix and Hilbert transform (IEVDHM–HT). In the proposed method, first the authors decompose non‐stationary signals using the IEVDHM with suitably defined criterion for eigenvalue selection, requirement of number of iterations, and new component merging criteria. Furthermore, the HT is applied on extracted components in order to obtain the TFR of non‐stationary signals. The performance of proposed TFR has been evaluated on synthetic signals in clean and white noise environment with different signal‐to‐noise ratios. The proposed method gives good performance in terms of Rényi entropy measure in comparison with other existing methods. Application of the proposed TFR is also shown for the classification of epileptic seizure electroencephalogram (EEG) signals. The least‐square support vector machine (LS‐SVM) with radial basis function kernel is used for classification of seizure and seizure‐free EEG signals obtained from the publicly available database by the University of Bonn, Germany. The proposed method has achieved classification accuracy 100% for the studied EEG database.

The time-series forecasting makes a substantial contribution in timely decision making. In this article, a recently developed eigenvalue decomposition of Hankel matrix (EVDHM) along with the autoregressive integrated moving average (ARIMA) is applied to develop a forecasting model for non-stationary time series. The Phillips-Perron test (PPT) is used to define the non-stationarity of time series. EVDHM is applied over a time-series to decompose it into respective sub-components and reduce the non-stationarity. ARIMA based model is designed to forecast the future values for each subcomponent. The forecasted values of each sub-component are added to get the final output values. Optimized value of ARIMA parameters for each sub-component is obtained using genetic algorithm (GA) for minimum values of Akaike Information Criterion (AIC). Model performance is evaluated by estimating the future values of daily new cases of the recent pandemic disease COVID-19 for India, United States America (USA), and Brazil. The high efficacy of proposed method is convinced with the results.

The use of radar technology in the field of human activity recognition (HAR) has garnered considerable interest due to its notable benefits in terms of accuracy, resilience, and safeguarding of privacy. As the back-scattered radar returns are composed of multiple components & non-stationary in behavior, the time-frequency analysis like Wigner-Ville distribution (WVD) can play a significant role, but the presence of cross-terms limits the suitability of WVD. This study introduces a time segmentation and frequency windowing-based novel strategy for cross-terms free WVD of multi-component non-stationary signals. The effectiveness of the proposed method is validated on synthetic signals which outperforms the existing related methods for different performance measures. The proposed TFR is also applied for HAR from the received signals of frequency-modulated continuous-wave (FMCW) radar. A novel analysis of extracting slow-time signatures from the received signal captured by FMCW radar is developed and the proposed technique is utilized to generate cross-term free TFRs from these signatures for each activity. Threshold-based time windowing followed by 2-D segmented features extraction is performed on the TFRs for activity recognition system development. The optimization of ensemble classifier yields an impressive classification accuracy rate of 99.51%, surpassing the performances achieved by previous methodologies on the same dataset.