Time-frequency representation of signals by wavelet transform

The aim of the data analysis is to explore the main characteristics of the signal by a signal transformation. The most commonly used way of analyzing the signals is the Fourier transform (FT). For stationary systems, where the signal properties over time do not change, the FT spectrum is easily interpreted. However, in cases where the systems change their physical properties and hence their characteristic spectrum in time, FT shows only the spectrum integrated over the acquisition time. As a consequence the modifications of the temporal signal are not directly correlated with the frequency features of the spectrum. For such non-stationary signals the method that combines the time and frequency domain analysis and hence shows the signal evolution in both time and frequency is needed. The windowed FT belongs to the family of techniques with such temporal and spectral resolution and it has been one of the first methods devised to operate in the time-frequency plane. However, windowed FT has the drawback of the fixed time-frequency resolution, because after the choice of a window function, the size of the time-frequency window is fixed. In contrary, the wavelet transform (WT) is a mathematical approach that gives the time-frequency representation of a signal with the possibility to adjust the time-frequency resolution, hence, WT may be considered as the time-frequency analysis method with an adjustable window, which is an improved alternative to the windowed FT. In the article, the advantages of WT in comparison with FT analysis are illustrated.