Using Hilbert Transform for biosignal samples ansamble statistical estimation


  • H. B. Tsupryk Ternopil Ivan Puluj National Technical University, Ternopil, Ukraine



biological object, excitation, response, Hilbert transform, coherence processing, quality estimate


For controlling and diagnosing of functional state, for correction functions of biological object the method of electrophysiological active research of this object often use. In particularly the use of low level light intensity (LLLI) for stimulation of biological object (information influence on biological object) is effective enough. The tendencies to reduce of light intensity is caused by necessity as comfortable conditions for biological object so and (in concordance with Weber-Fechner's law) increasing informativeness of response of that biological object. However, the ratio of response power to the noise power (RRN) is decreasing strongly after that. Decreasing intensity of stimulation is causing increasing of the initial (latent) part of the response of bio-object. In addition, the length of latent parts responses are stochastic. Therefore, there is a need of statistical estimation ensemble of these responses with aim to improve RRN. The standard method estimating of the response is the averaging of the responses, estimating the moment of first order of probability distribution function of values the responses. Estimating statistical characteristics of the response of bioobject on to LLLI stimulation using statistical processing of ensemble of the responses is the problem. Using interactive synchronization procedures, and synchronization automation by using perfusing blood or by heart rhythm greatly complicates both hardware and software. In this paper the ways for ensure coherences of the responses after the excitations of biological object which are in the general sample (in the ensemble) had been explored. The results of computer simulation of statistical test are obtained. Improvement of the quality of estimation of the mathematical expectation of ensemble of responses after Hilbert transform is detected. The results are used to automate the information-analytical systems of active research of biological objects.

Author Biography

H. B. Tsupryk, Ternopil Ivan Puluj National Technical University, Ternopil

Tsupyk H. B.





Theory and Practice of Radio Measurements