160 research outputs found
Time series classification based on fractal properties
The article considers classification task of fractal time series by the meta
algorithms based on decision trees. Binomial multiplicative stochastic cascades
are used as input time series. Comparative analysis of the classification
approaches based on different features is carried out. The results indicate the
advantage of the machine learning methods over the traditional estimating the
degree of self-similarity.Comment: 4 pages, 2 figures, 3 equations, 1 tabl
Long-range dependencies in heart rate signals- revisited
The RR series extracted from human electrocardiogram signal (ECG) is
considered as a fractal stochastic process. The manifestation of long-range
dependencies is the presence of power laws in scale dependent process
characteristics. Exponents of these laws: - describing power spectrum
decay, - responsible for decay of detrended fluctuations or
related to, so-called, roughness of a signal, are known to differentiate hearts
of healthy people from hearts with congestive heart failure. There is a strong
expectation that resolution spectrum of exponents, so-called, local exponents
in place of global exponents allows to study differences between hearts in
details. The arguments are given that local exponents obtained in multifractal
analysis by the two methods: wavelet transform modulus maxima (WTMM) and
multifractal detrended fluctuation analysis (MDFA), allow to recognize the
following four stages of the heart: healthy and young, healthy and advance in
years, subjects with left ventricle systolic dysfunction (NYHA I--III class)
and characterized by severe congestive heart failure (NYHA III-IV class).Comment: 24 page
Quantifying and containing the curse of high resolution coronal imaging
Future missions such as Solar Orbiter (SO), InterHelioprobe, or Solar Probe
aim at approaching the Sun closer than ever before, with on board some high
resolution imagers (HRI) having a subsecond cadence and a pixel area of about
at the Sun during perihelion. In order to guarantee their scientific
success, it is necessary to evaluate if the photon counts available at these
resolution and cadence will provide a sufficient signal-to-noise ratio (SNR).
We perform a first step in this direction by analyzing and characterizing the
spatial intermittency of Quiet Sun images thanks to a multifractal analysis.
We identify the parameters that specify the scale-invariance behavior. This
identification allows next to select a family of multifractal processes, namely
the Compound Poisson Cascades, that can synthesize artificial images having
some of the scale-invariance properties observed on the recorded images.
The prevalence of self-similarity in Quiet Sun coronal images makes it
relevant to study the ratio between the SNR present at SoHO/EIT images and in
coarsened images. SoHO/EIT images thus play the role of 'high resolution'
images, whereas the 'low-resolution' coarsened images are rebinned so as to
simulate a smaller angular resolution and/or a larger distance to the Sun. For
a fixed difference in angular resolution and in Spacecraft-Sun distance, we
determine the proportion of pixels having a SNR preserved at high resolution
given a particular increase in effective area. If scale-invariance continues to
prevail at smaller scales, the conclusion reached with SoHO/EIT images can be
transposed to the situation where the resolution is increased from SoHO/EIT to
SO/HRI resolution at perihelion.Comment: 25 pages, 1 table, 7 figure
Wavelet and Multiscale Analysis of Network Traffic
The complexity and richness of telecommunications traffic is such that one may despair to find any regularity or explanatory principles. Nonetheless, the discovery of scaling behaviour in tele-traffic has provided hope that parsimonious models can be found. The statistics of scaling behavior present many challenges, especially in non-stationary environments. In this paper we describe the state of the art in this area, focusing on the capabilities of the wavelet transform as a key tool for unravelling the mysteries of traffic statistics and dynamics
Multiscaling analysis and modelling of bursty impulsive noise in broadband power line communication channels.
Doctor of Philosophy in Electronic Engineering. University of KwaZulu-Natal, Durban 2017.Power line communication (PLC) networks have the potential to offer broadband
application services to homes and small offices cheaply since no additional
wiring is required for it implementation. However, like other communication systems,
it has its own challenges and the understanding of its channel characteristics
is key to its optimal performance evaluation and deployment. Multipath propagation
due to impedance mismatch and bursty impulsive noise are the important
challenges that must be understood and their effects minimized for optimal system
performance. Noise in power line communication networks is non-Gaussian and
as such cannot be modelled as the convenient additive white Gaussian noise. The
noise is known to be impulsive and in most cases, occurs in bursts. Therefore, it can
be referred as bursty impulsive noise. Due to unique nature of this noise in power
line channels, modulation and decoding schemes optimized for Gaussian channels
may not necessarily work well in PLC systems. Recently developed noise models
though take into consideration memory inherent in PLC noise, models capturing
both long range correlations and multiscaling behaviour are not yet available in
the literature. Furthermore, even though it is known that PLC noise has memory
(i.e., it is correlated), the statistical properties of it is not well documented in the
literature and will be the focus of this thesis.
In this thesis, multiscaling behaviour of PLC noise is investigated. Both fractal
and multifractal analysis methods are employed on noise data collected in three
different scenarios (small offices, stand-alone apartment and University electronic
laboratory) and their characteristics analysed. Multifractal analysis is employed
since it is able to characterize both the strengths and frequency of occurrence of
bursts in power line noise. Specifically, the contributions in this thesis are as follows:
Firstly, empirical evidence is provided that PLC noise clearly manifests long
range correlations behaviour. This is achieved by calculating the Hurst parameter
(which is a measure of self similarity) in data from the above scenarios. Various
methods employed to estimate this Hurst parameter reveal that in all the scenarios,
long range dependence is evidenced. Secondly, multifractal detrended fluctuation analysis (MDFA) and multifractal
detrending moving average (MDMA) analysis have been used to investigate the
temporal correlations and scaling behaviour of power line channel noise measured
from the three different scenarios mentioned earlier. Empirical results show that
power line noise clearly manifests both long-range correlation and multifractal scaling
behaviour with different strengths depending on the environments where they were captured. From the estimated singularity spectrum which is left truncated,
it is evident from the two methods used that power line noise is sensitive to small
fluctuations and is characterized by large scaling exponents. Multifractal analysis
of the reshuffled time series noise reveal that the multifractal nature of PLC noise
is as a result of long range correlation inherent in the noise and not from the heavy
tailed distributions in it.
Thirdly, we propose a multiplicative cascade model for PLC noise that is able
to reproduce the empirical findings concerning the PLC noise time series: its local
scaling behaviour and long range correlations. Model parameters are derived from
the shape of multifractal spectrum of the PLC time series noise collected from
measurement campaigns. Since in the recent past, the main challenge in PLC
systems has been on how to model bursty impulsive PLC noise, the proposed
model will be very useful in evaluating system performance of PLC networks in
the presence of the bursty impulsive noise inherent in PLC networks. Moreover,
bursts of different frequencies and strengths can be modelled by this proposed
model and hence their effects on system performance evaluated. This will also
open up investigations into designing modulation and decoding schemes that are
optimal in systems prone to bursty impulsive noise
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