Omega-dimension of chaotic time series.
New characteristics, Omega-dimension (D(Omega)) and spectral density of dimension (D'(Omega)), of deterministically generated irregular signals are proposed. They are the functions that are calculated employing spectral transformation such as filtering with limit transmission frequency Omega. The Omega-dimension of the time series generated by a dynamical system with a homogeneous strange attractor does not depend on Omega and coincides with the dimension measured using a standard technique. If the time series does not possess the similarity property as the time scale changes (i.e., it is multiscaled in time), the calculation of D(Omega) gives additional information on the properties of the signal. In particular, it allows for the estimation of additional degrees of freedom in the time series on signal transmission through the communication channel and preliminary processing.
Gaponov-Grekhov
A. V.
AV
Institute of Applied Physics, Russian Academy of Science, 46 Uljanov Street, 603600 Nizhniy Novgorod, RussiaRadiophysical Research Institute, 25/14 B. Pecherskaya Street, 603600 Nizhniy Novgorod, Russia.
Rabinovich
M. I.
MI
Starobinets
I. M.
IM
Tsimring
M. Sh.
MS
Chugurin
V. V.
VV