Time Frequency Analyses of stationary and non-stationary signals using MATLAB functions and Toolboxes)

Abstract Time-frequency analysis of non-stationary signals in a noisy environment is a challenging research subject spanning many areas, and often requires simultaneous signal decomposition in the time and frequency domains. Non-stationary signals are composed of numerous frequencies and irregularly changing amplitudes in time. Unlike sinusoidal waves, square waves, and other types of stationary signals, non-stationary signals do not have repeated patterns that can be easily characterized and modeled. The analysis of non-stationary signals requires a special methodological approach and mathematical means, which allow discovery and analysis of the main features of the non-stationary signal using signal transformation. The general method for signal analysis is to apply Fourier transformations. However, Fourier transform analysis provides actual spectra only for stationary signals. Also, the Fourier transform only provides information in the frequency domain without providing time information. For non-stationary signal analysis, the most valid methods are the Short Time Fourier Transform and wavelet transform. In this work, we investigate comprehensively different methodological approaches and mathematical tools for non-stationary analysis and compare these results when applied to stationary signals.