Journal ArticleDOI
Relationship between the fractal dimension and the power law index for a time series: a numerical investigation
Reads0
Chats0
TLDR
In this paper, the relationship between the power law index α and the fractal dimension D for a time series following a power law spectrum is investigated by using a numerical experiment, and the relationships between α and D are also examined both for the differenced and for the integrated time series.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1990-10-01. It has received 209 citations till now. The article focuses on the topics: Fractal dimension & Spectral density.read more
Citations
More filters
Journal ArticleDOI
A Review of Feature Extraction Methods in Vibration-Based Condition Monitoring and Its Application for Degradation Trend Estimation of Low-Speed Slew Bearing
TL;DR: In this paper, an empirical study of feature extraction methods for the application of low-speed bearing condition monitoring is presented, where the selected features such as impulse factor, margin factor, approximate entropy and largest Lyapunov exponent (LLE) show obvious changes in bearing condition from normal condition to final failure.
Journal ArticleDOI
Nonlinear dynamics of cardiovascular ageing
TL;DR: It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in dynamical terms.
Journal Article
Some Comments on the Correlation Dimension of 1/fαNoise
TL;DR: In this paper, it was shown that a stochastic (infinite degree of freedom) time series with a 1/fα power spectrum can exhibit a finite correlation dimension even for arbitrarily large data sets.
Journal ArticleDOI
Spatiotemporal analysis of prepyriform, visual, auditory, and somesthetic surface EEGs in trained rabbits
TL;DR: Spatial ensemble averages were computed for 64 traces of electroencephalograms simultaneously recorded from 8 x 8 arrays over the epidural surfaces of the prepyriform cortex and visual, somatic, and auditory cortices to reveal a common waveform common to all 64 EEGs from an array.
Journal ArticleDOI
Some comments on the correlation dimension of 1/fα noise
TL;DR: In this paper, the scaling of the correlation integral C(n, r) in various regimes of the (N, r)-plane is analyzed for Gausian 1/fα noise, with explicit high and low frequency cutoffs.
References
More filters
Journal ArticleDOI
A mathematical theory of communication
TL;DR: This final installment of the paper considers the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now.
Book
Fractals: Form, Chance and Dimension
TL;DR: Fractals as mentioned in this paper is a new field of mathematics that models the most interdisciplinary grab-bag of naturally occurring forms, such as coastlines and clouds, crystals, snowflakes and cosmological structures.
Journal ArticleDOI
Approach to an irregular time series on the basis of the fractal theory
TL;DR: In this article, the fractal dimension of the set of points (t, f(t)) forming the graph of a function f defined on the unit interval was measured using a self-similarity property.
Book
The geometry of fractal sets
TL;DR: In this paper, a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension is presented, including questions of local density and the existence of tangents of such sets, and the dimensional properties of their projections in various directions.
Book ChapterDOI
Prediction and Entropy
TL;DR: The emergence of the magic number 2 in recent statistical literature is explained by adopting the predictive point of view of statistics with entropy as the basic criterion of the goodness of a fitted model.