Zastosowanie funkcji bispektrum do analizy danych pomiarowych

W pracy omówiono zastosowanie funkcji bispektrum oraz metod statystyki wielowymiarowej do analizy danych pomiarowych ewidencjonowanych w warunkach oddziaływania niekontrolowanych zakłóceń na środowisko pomiarowe.

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When dealing with signals that exhibit irregular behavior, the most widely accepted approach consists of modelling it as the realization of some stochastic process. Because of the nature of these classes of signals, higher order techniques are likely to play an important role in algorithms aimed at processing them in the measuring systems. The higher order spectra (also known as polyspectra), defined in terms of higher order statistics (cumulants) of a signal are atractive since no special assumptions on the underlying signal model are necessary. There are several general motivations behind the use of the higher order spectra in signal processing. These include techniques to: (1) suppress additive colored Gaussian noise of unknown power spectrum; (2) identify nonminimum phase systems or reconstruct nonminimum phase signals; (3) extract information due to deviations from Gaussianity; (4) detect and characterize nonlinear properties in signals as well as identify nonlinear systems. The particular cases of the higher order spectra is the third order spectrum also called the bispectrum, which is the Fourier transform of the third order statistics. This paper is devoted to the study of bispectrum for explorative analysis of the measuring data, collected in the conditions, when measuring signals are corrupted by nonidentiflcable disturbations in measuring process. The algorithm based on multidimensional analysis measuring data has been proposed. The deciles of the distribution of bispectrum in their principal domain have been used as distinctive features for data set classification. An example of data analysis collected in underwater environment has been discussed.