O. N. Pavlova

Analysis of correlation properties of random processes using short signals

The possibility of studying the correlation properties of random processes within the framework of a multifractal formalism is considered. It is shown that the calculation of Hölder exponents allows one to judge on the correspondence of an analyzed signal to a process with known statistical properties using a significantly smaller amount of experimental data as compared to that necessary for evaluating the law of correlation decay by means of calculations of the autocorrelation function.

Estimating the predictability time of noisy chaotic dynamics from point sequences

A method for increasing the accuracy of estimation of the predictability time of noisy chaotic dynamics from system-related point sequences is proposed. General laws observed in the application of this method to interspike interval series of model threshold devices of two types operating in the regime of phase-coherent chaos are illustrated.

Speech signal filtration using double-density dual-tree complex wavelet transform

We consider the task of increasing the quality of speech signal cleaning from additive noise by means of double-density dual-tree complex wavelet transform (DDCWT) as compared to the standard method of wavelet filtration based on a multiscale analysis using discrete wavelet transform (DWT) with real basis set functions such as Daubechies wavelets. It is shown that the use of DDCWT instead of DWT provides a significant increase in the mean opinion score (MOS) rating at a high additive noise and makes it possible to reduce the number of expansion levels for the subsequent correction of wavelet coefficients.

Noisy signal filtration using complex wavelet basis sets

Methods of noisy signal filtration using a discrete wavelet transform (DWT) with real basis sets of the Daubechies family are compared to methods employing a double-density dual-tree complex wavelet transform (DDCWT) with excess (nonorthonormalized) basis sets. Recommendations concerning the choice of filter parameters for minimization of the error of noisy signal filtration are formulated.

Analysis of chaotic dynamic regimes using series of interburst intervals

The problem of reconstruction of dynamic systems in the presence of noise using series of interburst intervals is solved. It is shown that the reconstruction procedure can be applied to strongly nonlinear noisy oscillatory processes. The results make it possible to generalize the method for analysis of dynamic systems with respect to recovery time to a wide variety of neuron oscillators.

Diagnostics of the regime of hyperchaotic dynamics from sequences of threshold-crossing time intervals

We consider a method of hyperchaotic regime diagnostics in a system with self-sustained oscillations by monitoring point processes representing sequences of time intervals between the moments at which the system response signal crosses a threshold level. The possibility of determining two positive Lyapunov exponents from a single point process of short duration is demonstrated.

Computing Spectral Characteristics from Short Signals and Nonstationary Processes

We propose a method of estimating spectral properties of a system from short signals and processes with varying characteristics, which is based on the wavelet-transform modulus-maxima method. It is shown that this approach allows significant reduction of the computing error as compared with the classical spectral analysis.

The Influence of Data Loss on Diagnostics of Complex System Dynamics

We consider the problem of quantitative description of the dynamics of complex systems using experimental data records containing various breakdown regions related to artifacts, violations of the operation conditions, or monitoring of equipment malfunctions. Elimination (rejection) of these regions can lead to modification of the signal structure, which makes it necessary to assess the influence of this procedure on the quantitative characteristics that are to be determined. An example of multiscale analysis of cerebral blood flow is presented, which shows that the correct diagnostics of the regime of system functioning may be possible even with extreme loss of data.

A Method for Increasing the Accuracy in Calculating the Characteristics of Complex Dynamics of Threshold Systems

The problem of increasing the accuracy of calculating the characteristics of complex dynamics in threshold systems is solved using the example of Lyapunov’s exponents. Despite the existence of theoretical and numerical studies that earlier have allowed one to substantiate the possibility of recovery of dynamic systems from the signals at the output of threshold systems, the problem of diagnostics of dynamics in the case of a small amount of data in the presence of noise requires a separate study. It has been shown how preliminary data processing that provides the transition to uniform sampling can significantly reduce the computation errors.

Errors of analysis of parameters of complex oscillation regimes using point sequences of the integrate-and-fire model

The problem of calculation of dynamical parameters of chaotic regimes of self-sustained oscillations using point processes is discussed. The “integrate-and-fire” model is used to exemplify the constraints of the method for attractor reconstruction using a sequence of time intervals between the time instants of pulse generation. The conditions of validity for calculation of the largest Lyapunov exponent and recommendations for the most accurate determination of dynamical parameters for complex oscillatory regimes in dynamical systems reconstruction using point processes are formulated.