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Time-frequency transformations of signals for the design system of multi-parameter analysis


A.I. Sherstobitov, V.I. Marchuk, M.P. Malinis, S.A. Gridin

In this paper we consider linear time-frequency transform such as the Gabor windowed Fourier transform and nonlinear class of Cohen. We study their characteristics and properties. We consider a field of using time-frequency transformations. Researches have shown that the field of the time-frequency transformations is vast and not limited to the analysis of non stationary signals. In order to study the resolution of the considered time-frequency transforms, set of models test signals are generated (dual-frequency signal, linearly frequency-modulated signal (chirp signal) and tone-frequency modulated signal (tone FM signal)), which differ in spectral composition. The graphs of the spectrum of test signals obtained by linear and nonlinear time-frequency Gabor transform and the Choi-Williams, respectively are presented. Accuracy representation of test signals are researched in the case of linear and nonlinear time-frequency transform by criteria standard deviation, and the results are summarized in the table. Based on studies of time-frequency spectrums and estimates of accuracy of the representation test signal in the case of linear and nonlinear transformations is formed recommendations about the use of spectrum time-frequency transformations to increase the amount of information about the parameters and composition of the decomposed signal components at various local areas.

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