M.D. Alekhin - researcher of Remote Sensing Laboratory of Bauman Moscow State Technical University

Comparative analysis of time-frequency transforms in a task of non-stationary quasi-periodic signal processing is carried out based on systematization of their general characteristics. Trial results of implementation of time-frequency transforms for analysis of a test non-stationary low-frequency biomedical signal are considered. Benefits and disadvantages of practical application of each of them are summarized. Linear time-frequency transforms such as short-time Fourier transform and Gabor transform are considered to have not satisfactory characteristics of localization in both time and frequency domains. Generally, proper frequency resolution corresponds to decrease of time localization, and vice versa. In turn, bilinear time-frequency transforms have rather good characteristics of localization in time and frequency domains but at the same time their significant disadvantage is an appearance of strong interference components. In modified bilinear transforms of Wigner and Bertran groups elimination of interference is performed on the base of application of time and frequency smoothing windows, but it subsequently leads to decrease of corresponding resolution characteristics. The latter circumstance reduces the overall benefits and prospects of application of this group of time-frequency transforms in practical tasks of wave structure analysis of non-stationary quasi-periodic signals. Relatively high complexity and a lack of fast calculation algorithms for implementation of bilinear time-frequency transforms significantly hamper their advantages in practical applications of non-stationary quasi-periodic signal processing tasks in real-time mode. To date wavelet transform is supposed to have one of the best time-frequency localization, which provides its high efficiency in ex-tracting of informative features in the tasks of pattern recognition for non-stationary quasi-periodic signals. The wide range of existing wavelet bases, gives the opportunity to select the optimal one taking into consideration the character of local peculiarities and properties of decomposition of analyzed non-stationary quasi-periodic signals.

 

1. Bogomolov A.V., Majjstrov A.I. Modelirovanie ritmokardiograficheskikh signalov v chastotnojj oblasti // Dinamika slozhnykh sistem - XXIvek. 2009. №1. S. 49−59.
2. Cohen L. Generalized Phase-space Distribution Functions // Journal of Mathematical Physics. 1966. V. 7. P. 781−786.
3. Morlet J., Arens G., Fourgeau I., Giard D. Wave Propagation and Sampling Theory // Geophysics. 1982. V. 47. P. 203−236.
4. Aljokhin M.D. Procedura opredelenija optimalnykh parametrov vejjvlet-preobrazovanija i nejjrosetevogo klassifikatora dlja povyshenija ehffektivnosti raspoznavanija patternov nestacionarnykh bioradiolokacionnykh signalov // Nejjrokompjutery: razrabotka, primenenie. 2012. № 6. C. 46−54.
5. SHerstobitov A.I., Marchuk V.I., Malinis M.P., Gridin S.A. CHastotno-vremennye preobrazovanija signalov dlja postroenija sistemy mnogoparametricheskogo analiza // Nelinejjnyjj mir. 2012. № 11. C. 762−768.
6. Lazorenko O.V., CHernogor L.F. Sistemnyjj spektralnyjj analiz signalov: teoreticheskie osnovy i prakticheskie primenenija // Radiofizika i radioastronomija. 2007. №2. S. 162−181.
7. Auger F., Flandrin P., Goncalves P., Lemoine O. Time-Frequency Toolbox Reference Guide. Rice University Publishing. 2005.