Abstract
We use the analytic signal approach based on the Hilbert transform to compute the phase difference between two non-stationary signals and find out epochs of phase locking.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Crutchfield J., Farmer D., Packard N., Shaw R., Jones G., Donelly R.J. (1980): Power spectral analysis of a dynamical system. Phys. Lett. A 76, 1–4
Feldman M.S. (1985): Investigation of the natural vibrations of machine elements using the Hilbert transform. Sov. Machine Sci. 2, 44–47
Feldman M.S. (1994): Nonlinear system vibration analysis using Hilbert transform I. Free vibration analysis method “FREEVIB”. Mech. Systems and Signal Processing 8, 119–127
Feldman M.S., Rosenblum M.G. (1988): Computer program for determination of nonlinear elastic and damping properties of a vibrating system. In Proceedings of the Workshop “Software in Machine Building CAD Systems”, 89. Izhevsk, 1988, (In Russian)
Fuchs A., Jirsa V., Haken H., Kelso J.S. (1996): Extending the HKB model of coordinated movement to oscillators with different eigenfrequencies. Biol. Cybern. 74, 21–30
Gabor D. (1946): Theory of communication. J. IEE London 93, 429–457
Little J.N., Shure L. (1992): Signal Processing Toolbox for Use with MATLAB. User’s Guide. Mathworks, Natick, MA
Panter P. (1965): Modulation, Noise, and Spectral Analysis. McGraw-Hill, New York
Parlitz U., Junge L., Lauterborn W., Kocarev L. (1996): Experimental observation of phase synchronization. Phys. Rev. E. 54, 2115–2118
Pikovsky A.S., Rosenblum M.G., Kurths J. (1996): Synchronization in a population of globally coupled chaotic oscillators. Europhys. Lett. 34, 165–170
Pikovsky A.S., Rosenblum M.G., Osipov G.V., Kurths J. (1997): Phase synchronization of chaotic oscillators by external driving. Physica D, 104, 219–238
Pompe B. (1993): Measuring statistical dependencies in a time series. J. Stat. Phys. 73, 587–610
Rabiner R, Gold B. (1975): Theory and Application of Digital Signal Processing. Prentice-Hall, Englewood Cliffs, NJ
Rosenblum M.G., Pikovsky A.S., Kurths J. (1996): Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 76, 1804–1807
Schieck M. (1994): Quantifizierung und Modellierung der respiratorischen Sinusarrhythmie. Technical Report 2899, Forschungszentrum Juelich, Juelich
Smith M.J., Mersereau R.M. (1992): Introduction to Digital Signal Processing. A Computer Laboratory Textbook. Wiley, New York
Tass P., Wunderlin A., Schanz M. (1995): A theoretical model of sinusoidal forearm tracking with delayed visual feedback. J. Biol. Phys. 21, 83–112
Tass P., Kurths J., Rosenblum M.G., Guasti G., Hefter H. (1996): Delay induced transitions in visually guided movement. Phys. Rev. E 54, 2224–2227
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rosenblum, M., Kurths, J. (1998). Analysing Synchronization Phenomena from Bivariate Data by Means of the Hilbert Transform. In: Kantz, H., Kurths, J., Mayer-Kress, G. (eds) Nonlinear Analysis of Physiological Data. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71949-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-71949-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-71951-6
Online ISBN: 978-3-642-71949-3
eBook Packages: Springer Book Archive