978 research outputs found
Wavelets and their use
This review paper is intended to give a useful guide for those who want to
apply discrete wavelets in their practice. The notion of wavelets and their use
in practical computing and various applications are briefly described, but
rigorous proofs of mathematical statements are omitted, and the reader is just
referred to corresponding literature. The multiresolution analysis and fast
wavelet transform became a standard procedure for dealing with discrete
wavelets. The proper choice of a wavelet and use of nonstandard matrix
multiplication are often crucial for achievement of a goal. Analysis of various
functions with the help of wavelets allows to reveal fractal structures,
singularities etc. Wavelet transform of operator expressions helps solve some
equations. In practical applications one deals often with the discretized
functions, and the problem of stability of wavelet transform and corresponding
numerical algorithms becomes important. After discussing all these topics we
turn to practical applications of the wavelet machinery. They are so numerous
that we have to limit ourselves by some examples only. The authors would be
grateful for any comments which improve this review paper and move us closer to
the goal proclaimed in the first phrase of the abstract.Comment: 63 pages with 22 ps-figures, to be published in Physics-Uspekh
Intermittent process analysis with scattering moments
Scattering moments provide nonparametric models of random processes with
stationary increments. They are expected values of random variables computed
with a nonexpansive operator, obtained by iteratively applying wavelet
transforms and modulus nonlinearities, which preserves the variance. First- and
second-order scattering moments are shown to characterize intermittency and
self-similarity properties of multiscale processes. Scattering moments of
Poisson processes, fractional Brownian motions, L\'{e}vy processes and
multifractal random walks are shown to have characteristic decay. The
Generalized Method of Simulated Moments is applied to scattering moments to
estimate data generating models. Numerical applications are shown on financial
time-series and on energy dissipation of turbulent flows.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1276 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields
The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282â288) to the two-dimensional (2D) fractional Brownian ïŹeld. In particular, we deïŹned Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefïŹcients over the levels of resolutions. Using the same methodology. we also deïŹned two other entropies in 2D: Tsallis and the RĂ©nyi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2) self-similar processes
Methods for characterising microphysical processes in plasmas
Advanced spectral and statistical data analysis techniques have greatly
contributed to shaping our understanding of microphysical processes in plasmas.
We review some of the main techniques that allow for characterising fluctuation
phenomena in geospace and in laboratory plasma observations. Special emphasis
is given to the commonalities between different disciplines, which have
witnessed the development of similar tools, often with differing terminologies.
The review is phrased in terms of few important concepts: self-similarity,
deviation from self-similarity (i.e. intermittency and coherent structures),
wave-turbulence, and anomalous transport.Comment: Space Science Reviews (2013), in pres
Non-invasive algorithm for bowel motility estimation using a back-propagation neural network model of bowel sounds
<p>Abstract</p> <p>Background</p> <p>Radiological scoring methods such as colon transit time (CTT) have been widely used for the assessment of bowel motility. However, these radiograph-based methods need cumbersome radiological instruments and their frequent exposure to radiation. Therefore, a non-invasive estimation algorithm of bowel motility, based on a back-propagation neural network (BPNN) model of bowel sounds (BS) obtained by an auscultation, was devised.</p> <p>Methods</p> <p>Twelve healthy males (age: 24.8 ± 2.7 years) and 6 patients with spinal cord injury (6 males, age: 55.3 ± 7.1 years) were examined. BS signals generated during the digestive process were recorded from 3 colonic segments (ascending, descending and sigmoid colon), and then, the acoustical features (jitter and shimmer) of the individual BS segment were obtained. Only 6 features (<it>J<sub>1, 3</sub>, J<sub>3, 3</sub>, S<sub>1, 2</sub>, S<sub>2, 1</sub>, S<sub>2, 2</sub>, S<sub>3, 2</sub></it>), which are highly correlated to the CTTs measured by the conventional method, were used as the features of the input vector for the BPNN.</p> <p>Results</p> <p>As a results, both the jitters and shimmers of the normal subjects were relatively higher than those of the patients, whereas the CTTs of the normal subjects were relatively lower than those of the patients (<it>p </it>< 0.01). Also, through <it>k</it>-fold cross validation, the correlation coefficient and mean average error between the CTTs measured by a conventional radiograph and the values estimated by our algorithm were 0.89 and 10.6 hours, respectively.</p> <p>Conclusions</p> <p>The jitter and shimmer of the BS signals generated during the peristalsis could be clinically useful for the discriminative parameters of bowel motility. Also, the devised algorithm showed good potential for the continuous monitoring and estimation of bowel motility, instead of conventional radiography, and thus, it could be used as a complementary tool for the non-invasive measurement of bowel motility.</p
A Partial Discharge Measurement Technique for Applied Square Pulse Voltage with 50 NS Rise Times
During the fabrication of solid electrical insulation, small cavities known as micro voids may form in the material. As electrical stress increases in this micro void, the breakdown probability also increases. This type of electrical breakdown is commonly known as partial discharge. Magnitudes of partial discharge currents are typically small but enough to cause degradation of the electrical insulation. To study degradation for fast-rise time voltage square pulse train, partial discharge measurement is needed. In current studies, partial discharge pulse widths have been measured in the range of nanoseconds. The best approach for measurement at ultra wide band frequencies is a bridge type measurement system, to reduce external noise and improve sensitivity to PD currents. The bridge configuration can be used with samples instead of one sample and one coupling capacitor. Identically created samples will have a close match for impedance and frequency response. This type of bridge also helps to reduce other sources of measured current such as the high displacement currents due to fast rise time square pulse voltage on the samples. Further improvement includes simultaneous measurements using a âlinkedâ bridge configuration, where bridges share a common sample. A directly connected measurement current shunt should be used for high sensitivity with a uniform ultra wide band frequency response. Post-measurement digital signal processing (DSP) algorithms will perform the task of pulse discrimination and time delay from the pulse front. This research presents a method to improve the measurement of partial discharge when applied voltage is non-sinusoidal, with high frequency components. The improvements are apparent when square pulse voltage rise times are less than 50 ns. Ultra wide band measurements of physical samples will be performed for short time duration with a digital storage oscilloscope. A DSP algorithm is used to filter residual noise from the partial discharge current. The presented measurement technique for samples for this study is an original approach. Sample results demonstrate the effectiveness of the technique
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