Time–Frequency Characterization of Non-Stationary Signals Using Adaptive Wavelet Transform Techniques

Abstract

Examples of non-stationary signals are commonly found in many scientific and engineering applications, such as biomedical monitoring, wireless communications, radar systems, speech processing, seismic exploration, and industrial fault diagnosis. The spectral characteristics of a non-stationary signal change as function of time; it is more difficult to correctly analyse them with conventional frequency-domain methods like Fourier Transform. The Short-Time Fourier Transform (STFT) is a method that can provide joint time–frequency analysis however, it has a fixed window size which cannot resolve complex signals to be both temporally and frequency resolved to provide high resolution analysis. The aim of this study is to propose an Adaptive Wavelet Transform (AWT)-based scheme for the time–frequency characterization of non-stationary signals to overcome the above disadvantages. The proposed approach is based on the multi-resolution analysis feature of the Continuous Wavelet Transform (CWT) which allows to capture the behavior of the signal at several scales and adapt the different parameters of the wavelet to the local characteristics of the signal. This adaptive mechanism aids localization of transients, variations in frequency and time-varying spectral components. The framework includes signal preprocessing, adaptive wavelet decomposition, estimation of the instantaneous frequency, energy distribution analysis, and feature extraction, ensuring a comprehensive characterization of the signal. The new method is tested using both synthetic and real-world non-stationary data sets. Time–frequency resolution, the accuracy of frequency estimation, the quality of signal reconstruction, the robustness to noise, and computational efficiency are used as assessment methods for performance. Experimental results show that the adaptive wavelet transform is more efficient to localize the features of the signal and the instantaneous frequency estimated than the traditional STFT, the Empirical Mode Decomposition (EMD) and the Synchrosqueezing Transform (SST). The proposed framework shows high robustness in noisy environment and is able to capture dynamic spectral variations in complex signals. Moreover, applicability of Adaptive Wavelet Based Time–Frequency Characterization is discussed in Biomedical Signal Analysis, Communication Systems, Radar Signal Processing, Structural Health Monitoring and Intelligent Sensing Applications. The results demonstrate that adaptive wavelet transform techniques are a powerful and flexible tool to analyze time–frequency characteristics of non-stationary signals with high-resolution while maintaining their advantages in digital signal processing for next-generation digital signal processing systems and intelligent analysis of real-time signals.