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Time-frequency analysis of non-stationary signals by wavelet-transform and windowed Fourier transform methods

DOI 10.18127/j00338486-201906(8)-03

Keywords:

N.V. Astakhov – Ph.D.(Eng.), Associate Professor, Department Radio Equipment Engineering and Manufacturing, Voronezh State Technical University
E-mail: kokakoller@gmail.com
A.V. Bashkirov – Dr.Sc.(Eng.), Associate Professor, Acting Head, Department Radio Equipment Engineering and Manufacturing, Voronezh State Technical University
E-mail: fabi7@mail.ru
O.E. Zhurilova – Post-graduate Student, Department Radio Equipment Engineering and Manufacturing, Voronezh State Technical University
E-mail: Suslovaoe@yandex.ru
O.Yu. Makarov – Dr.Sc.(Eng.), Professor, Department Radio Equipment Engineering and Manufacturing, Voronezh State Technical University
E-mail: mou@hotbox.ru


The time-frequency analysis of non-stationary signals by the methods of wavelet transform and window Fourier transform is considered. Simulation of a nonstationary signal and its time-frequency analysis in the computer mathematics system MATLAB were carried out. The process and results of modeling are described in detail, the advantages and disadvantages of each method are revealed. In the method of window Fourier transform, the effect of windows of different sizes on the representation of the signal in the time-frequency domain is investigated, in the wavelet transform method, the influence of the choice of the mother wavelet on the simulation results is considered.
Frequency methods of spectral analysis do not allow to determine the time of existence of the frequency in the process, which leads to limited opportunities in the analysis of non-stationary frequency processes. To solve many problems of spectral analysis of signals, a signal is required in both the frequency and time domains. This is necessary for analyzing signal changes over time, identifying local features (steps, discontinuities, peaks), short-term and global patterns.
This article describes the time-frequency analysis methods of the window Fourier transform and wavelet transform. Simulation of a nonstationary signal and its time-frequency analysis in the computer mathematics system MATLAB were carried out. In the method of window Fourier transform, the effect of windows of different sizes on the representation of the signal in the time-frequency domain is investigated, in the wavelet transform method, the influence of the choice of the mother wavelet on the simulation results is considered. The results of the window Fourier transform with a wide and narrow Hamming window showed that the wider the window size, the better the frequency resolution, but the worse the time, and vice versa. The article describes the wavelet transform with different maternal wavelets: Morlеtand Mexican Hat. The simulation showed that the Morlet wavelet has a higher frequency resolution, and the Mexican hat wavelet has a time. Also, as a result of the simulation, it was concluded that in the low-frequency region the wavelet transform has better frequency resolution and worse in time, and in the high-frequency region better resolution in time and worse in frequency, and the choice of a particular wavelet only slightly improves the resolution in the required region.
The study revealed the advantages and disadvantages of each method. The disadvantage of the window Fourier transform is the window width of fixed window functions, as a result of which the resolution is lost either in frequency or in time. However, the Fourier transform is used more often due to the greater knowledge and efficiency of the algorithms. Wavelet transform is well suited for the effective detection of various features of signals, the identification of short-term and global patterns.

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