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Register a new userAnalysis of Discrete Signals with Stochastic Components using Flicker Noise Spectroscopy
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The problem of information extraction from discrete stochastic time series, produced with some finite sampling frequency, using flicker-noise spectroscopy, a general framework for information extraction based on the analysis of the correlation links between signal irregularities and formulated for continuous signals, is discussed. It is shown that the mathematical notions of Dirac and Heaviside functions used in the analysis of continuous signals may be interpreted as high-frequency and low-frequency stochastic components, respectively, in the case of discrete series. The analysis of electroencephalogram measurements for a teenager with schizophrenic symptoms at two different sampling frequencies demonstrates that the power spectrum and difference moment contain different information in the case of discrete signals, which was formally proven for continuous signals. The sampling interval itself is suggested as an additional parameter that should be included in general parameterization procedures for real signals.
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This review presents the fundamentals of Flicker-Noise Spectroscopy (FNS), a general phenomenological methodology in which the dynamics and structure of complex systems, characterized by nonlinear interactions, dissipation, and inertia, are analyzed by extracting information from various signals with stochastically varying components generated by the systems. The basic idea of FNS is to treat the correlation links present in sequences of different irregularities, such as spikes, jumps, and discontinuities in derivatives of different orders, on all levels of the spatiotemporal hierarchy of the system under study as main information carriers. The tools to extract and analyze the information are power spectra and difference moments (structural functions) of various orders. Presently, FNS can be applied to three types of problems: (1) determination of parameters or patterns that characterize the dynamics or structural features of complex systems; (2) finding precursors of abrupt changes in the state of various complex systems based on a priori information about the dynamics of the systems; and (3) determination of flow dynamics in distributed systems based on the analysis of dynamic correlations in stochastic signals that are simultaneously measured at different points in space. Examples of FNS applications to such problems as parameterization of the images produced with atomic force microscopy (AFM), determination of precursors for electric breakdowns and major earthquakes, and analysis of electric potential fluctuations in electromembrane systems, as well as to some other problems in electrochemistry and medicine are discussed.
We use flicker-noise spectroscopy (FNS), a phenomenological method for the analysis of time and spatial series operating on structure functions and power spectrum estimates, to identify and study harmful chatter vibrations in a regenerative turning process. The 3D cutting force components experimentally measured during stainless steel turning are analyzed, and the parameters of their stochastic dynamics are estimated. Our analysis shows that the system initially exhibiting regular vibrations associated with spindle rotation becomes unstable to high-frequency noisy oscillations (chatter) at larger cutting depths. We suggest that the chatter may be attributed to frictional stick-and-slip interactions between the contact surfaces of cutting tool and workpiece. We compare our findings with previously reported results obtained by statistical, recurrence, multifractal, and wavelet methods. We discuss the potential of FNS in monitoring the turning process in manufacturing practice.
A phenomenological systems approach for identifying potential precursors in multiple signals of different types for the same local seismically active region is proposed based on the assumption that a large earthquake may be preceded by a system reconfiguration (preparation) at different time and space scales. A nonstationarity factor introduced within the framework of flicker-noise spectroscopy, a statistical physics approach to the analysis of time series, is used as the dimensionless criterion for detecting qualitative (precursory) changes within relatively short time intervals in arbitrary signals. Nonstationarity factors for chlorine-ion concentration variations in the underground water of two boreholes on the Kamchatka peninsula and geacoustic emissions in a deep borehole within the same seismic zone are studied together in the time frame around a large earthquake on October 8, 2001. It is shown that nonstationarity factor spikes (potential precursors) take place in the interval from 70 to 50 days before the earthquake for the hydrogeochemical data and at 29 and 6 days in advance for the geoacoustic data.
The flicker-noise spectroscopy (FNS) approach is used to determine the dynamic characteristics of neuromagnetic responses by analyzing the magnetoencephalographic (MEG) signals recorded as the response of a group of control human subjects and a patient with photosensitive epilepsy (PSE) to equiluminant flickering stimuli of different color combinations. Parameters characterizing the analyzed stochastic biomedical signals for different frequency bands are identified. It is shown that the classification of the parameters of analyzed MEG responses with respect to different frequency bands makes it possible to separate the contribution of the chaotic component from the overall complex dynamics of the signals. It is demonstrated that the chaotic component can be adequately described by the anomalous diffusion approximation in the case of control subjects. On the other hand, the chaotic component for the patient is characterized by a large number of high-frequency resonances. This implies that healthy organisms can suppress the perturbations brought about by the flickering stimuli and reorganize themselves. The organisms affected by photosensitive epilepsy no longer have this ability. This result also gives a way to simulate the separate stages of the brain cortex activity in vivo. The examples illustrating the use of the FNS device for identifying even the slightest individual differences in the activity of human brains using their responses to external standard stimuli show a unique possibility to develop the individual medicine of the future.
We study the dependence of the spectral density of the covariance matrix ensemble on the power spectrum of the underlying multivariate signal. The white noise signal leads to the celebrated Marchenko-Pastur formula. We demonstrate results for some colored noise signals.
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