Skip to main content
main-content
Top

Hint

Swipe to navigate through the articles of this issue

Published in: Measurement Techniques 12/2022

02-05-2022 | RADIO MEASUREMENTS

Determination of Probabilistic Characteristics of Random Values of Estimates of the Lyapunov Function for Description of a Physical Process

Authors: Yu. M. Veshkurtsev, D. A. Titov

Published in: Measurement Techniques | Issue 12/2022

Login to get access
share
SHARE

Abstract

Application of the Lyapunov characteristic function is determined by the means for estimating it. The probabilistic characteristics of estimates of the Lyapunov characteristic function are described for the first time. The probabilistic characteristics of random values of estimates of the Lyapunov function are estimated empirically by statistical methods. A model of a special device for producing estimates of the characteristic function by a direct method is developed in the Matlab package. A quasi-deterministic signal is delivered to the input of the model for which the instantaneous values are distributed according to an arcsine law and at the output a set of values of estimates of the Lyapunov function is obtained which is used to evaluate the probabilistic characteristics of these estimates. Statistical evaluation is carried out by an indirect method. It is found that the values of the estimates of the Lyapunov characteristic function are distributed according to a normal law. The results of these studies will be of use for engineering calculations, e.g., in identifying the errors in transfer of messages in modems with a modulated characteristic function.
Literature
1.
go back to reference A. M. Lyapunov, Collected Works, AN SSSR (1954), Vol. 1, pp. 125–176. A. M. Lyapunov, Collected Works, AN SSSR (1954), Vol. 1, pp. 125–176.
2.
go back to reference C. L. Brown and A. V. Zoubir, “A new approach to testing Gaussianity with the characteristic function,” Trends in Information Systems Engineering and Wireless Multimedia Communications. 1997 Int. Conf. on Information, Communications, and Signal Processing, Singapore, Sept. 9–12, 1997, IEEE (1997), Vol. 2, pp. 1198–1202, https://​doi.​org/​ https://​doi.​org/​10.​1109/​ICICS.​1997.​652173. C. L. Brown and A. V. Zoubir, “A new approach to testing Gaussianity with the characteristic function,” Trends in Information Systems Engineering and Wireless Multimedia Communications. 1997 Int. Conf. on Information, Communications, and Signal Processing, Singapore, Sept. 9–12, 1997, IEEE (1997), Vol. 2, pp. 1198–1202, https://​doi.​org/​ https://​doi.​org/​10.​1109/​ICICS.​1997.​652173.
4.
go back to reference Parchami, H. Amindavar, and J. A. Ritcey, “Application of characteristic function to detection in sinusoidal interference plus Gaussian noise,” 2009 IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, Taipei, Taiwan, April 19–24, 2009, IEEE (2009), pp. 3057–3060, https://​doi.​org/​ https://​doi.​org/​10.​1109/​ICASSP.​2009.​4960269. Parchami, H. Amindavar, and J. A. Ritcey, “Application of characteristic function to detection in sinusoidal interference plus Gaussian noise,” 2009 IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, Taipei, Taiwan, April 19–24, 2009, IEEE (2009), pp. 3057–3060, https://​doi.​org/​ https://​doi.​org/​10.​1109/​ICASSP.​2009.​4960269.
6.
go back to reference V. S. Parshin, “Recognition of random signals when used as features of sample characteristic functions,” Dig. Sign. Process., No. 2, 29–34 (2019). V. S. Parshin, “Recognition of random signals when used as features of sample characteristic functions,” Dig. Sign. Process., No. 2, 29–34 (2019).
11.
go back to reference Yu. M. Veshkurtsev, Applied Analysis of the Characteristic Function of Stochastic Processes, Moscow, Radio i Svyaz, Moscow (2003). Yu. M. Veshkurtsev, Applied Analysis of the Characteristic Function of Stochastic Processes, Moscow, Radio i Svyaz, Moscow (2003).
12.
go back to reference B. V. Gnedenko, A Course in Probability Theory, Nauka, Moscow (1969). B. V. Gnedenko, A Course in Probability Theory, Nauka, Moscow (1969).
13.
go back to reference Yu. M. Veshkurtsev, N. D. Veshkurtsev, and E. I. Algazin, Patent No. 2626332 RF, Izobret. Polezn. Modeli, No. 21 (2017). Yu. M. Veshkurtsev, N. D. Veshkurtsev, and E. I. Algazin, Patent No. 2626332 RF, Izobret. Polezn. Modeli, No. 21 (2017).
14.
go back to reference B. R. Levin, Theoretical Foundations of Statistical Electronics, Sov. Radio, Moscow (1966). B. R. Levin, Theoretical Foundations of Statistical Electronics, Sov. Radio, Moscow (1966).
15.
go back to reference Yu. M. Veshkurtsev, N. D. Veshkurtsev, and D. A. Titov, Instrumentation Based on the Characteristic Function of Random Processes, Izd. ANS SibAK, Novosibirsk (2018). Yu. M. Veshkurtsev, N. D. Veshkurtsev, and D. A. Titov, Instrumentation Based on the Characteristic Function of Random Processes, Izd. ANS SibAK, Novosibirsk (2018).
16.
go back to reference V. I. Tihonov, Statistical Radio Engineering, Sov. Radio, Moscow (1966). V. I. Tihonov, Statistical Radio Engineering, Sov. Radio, Moscow (1966).
Metadata
Title
Determination of Probabilistic Characteristics of Random Values of Estimates of the Lyapunov Function for Description of a Physical Process
Authors
Yu. M. Veshkurtsev
D. A. Titov
Publication date
02-05-2022
Publisher
Springer US
Published in
Measurement Techniques / Issue 12/2022
Print ISSN: 0543-1972
Electronic ISSN: 1573-8906
DOI
https://doi.org/10.1007/s11018-022-02037-0