1,172 research outputs found
Magnetic turbulence in the plasma sheet
Small-scale magnetic turbulence observed by the Cluster spacecraft in the
plasma sheet is investigated by means of a wavelet estimator suitable for
detecting distinct scaling characteristics even in noisy measurements. The
spectral estimators used for this purpose are affected by a frequency dependent
bias. The variances of the wavelet coefficients, however, match the power-law
shaped spectra, which makes the wavelet estimator essentially unbiased. These
scaling characteristics of the magnetic field data appear to be essentially
non-steady and intermittent. The scaling properties of bursty bulk flow (BBF)
and non-BBF associated magnetic fluctuations are analysed with the aim of
understanding processes of energy transfer between scales. Small-scale ( s) magnetic fluctuations having the same scaling index as the large-scale ( s) magnetic fluctuations occur during
BBF-associated periods. During non-BBF associated periods the energy transfer
to small scales is absent, and the large-scale scaling index
is closer to Kraichnan or Iroshnikov-Kraichnan scalings. The anisotropy
characteristics of magnetic fluctuations show both scale-dependent and
scale-independent behavior. The former can be partly explained in terms of the
Goldreich-Sridhar model of MHD turbulence, which leads to the picture of
Alfv\'{e}nic turbulence parallel and of eddy turbulence perpendicular to the
mean magnetic field direction. Nonetheless, other physical mechanisms, such as
transverse magnetic structures, velocity shears, or boundary effects can
contribute to the anisotropy characteristics of plasma sheet turbulence. The
scale-independent features are related to anisotropy characteristics which
occur during a period of magnetic reconnection and fast tailward flow.Comment: 32 pages, 12 figure
Continuous Wavelet Transform and Hidden Markov Model Based Target Detection
Standard tracking filters perform target detection process by comparing the sensor output signal with a predefined threshold. However, selecting the detection threshold is of great importance and a wrongly selected threshold causes two major problems. The first problem occurs when the selected threshold is too low which results in increased false alarm rate. The second problem arises when the selected threshold is too high resulting in missed detection. Track-before-detect (TBD) techniques eliminate the need for a detection threshold and provide detecting and tracking targets with lower signal-to-noise ratios than standard methods. Although TBD techniques eliminate the need for detection threshold at sensorâs signal processing stage, they often use tuning thresholds at the output of the filtering stage. This paper presents a Continuous Wavelet Transform (CWT) and Hidden Markov Model (HMM) based target detection method for employing with TBD techniques which does not employ any thresholding
Fractal estimation using models on multiscale trees
Caption title.Supported by the Office of Naval Research. N00014-91-J-1004 Supported by the Advanced Research Projects Agency. F49620-93-1-0604 Supported by the Air Force Office of Scientific Research. F49620-95-1-0083 Supported by an NSERC-67 Fellowship of the Natural Sciences and Engineering Council of Canada. Includes bibliographical references (p. 7-8).Paul W. Fieguth, Alan S. Willsky
Reconstruction of sparse wavelet signals from partial Fourier measurements
In this paper, we show that high-dimensional sparse wavelet signals of finite
levels can be constructed from their partial Fourier measurements on a
deterministic sampling set with cardinality about a multiple of signal
sparsity
Analysis of observed chaotic data
Thesis (Master)--Izmir Institute of Technology, Electronics and Communication Engineering, Izmir, 2004Includes bibliographical references (leaves: 86)Text in English; Abstract: Turkish and Englishxii, 89 leavesIn this thesis, analysis of observed chaotic data has been investigated. The purpose of analyzing time series is to make a classification between the signals observed from dynamical systems. The classifiers are the invariants related to the dynamics. The correlation dimension has been used as classifier which has been obtained after phase space reconstruction. Therefore, necessary methods to find the phase space parameters which are time delay and the embedding dimension have been offered. Since observed time series practically are contaminated by noise, the invariants of dynamical system can not be reached without noise reduction. The noise reduction has been performed by the new proposed singular value decomposition based rank estimation method.Another classification has been realized by analyzing time-frequency characteristics of the signals. The time-frequency distribution has been investigated by wavelet transform since it supplies flexible time-frequency window. Classification in wavelet domain has been performed by wavelet entropy which is expressed by the sum of relative wavelet energies specified in certain frequency bands. Another wavelet based classification has been done by using the wavelet ridges where the energy is relatively maximum in time-frequency domain. These new proposed analysis methods have been applied to electrical signals taken from healthy human brains and the results have been compared with other studies
Spike detection using the continuous wavelet transform
This paper combines wavelet transforms with basic detection theory to develop a new unsupervised method for robustly detecting and localizing spikes in noisy neural recordings. The method does not require the construction of templates, or the supervised setting of thresholds. We present extensive Monte Carlo simulations, based on actual extracellular recordings, to show that this technique surpasses other commonly used methods in a wide variety of recording conditions. We further demonstrate that falsely detected spikes corresponding to our method resemble actual spikes more than the false positives of other techniques such as amplitude thresholding. Moreover, the simplicity of the method allows for nearly real-time execution
A scale-space approach with wavelets to singularity estimation
This paper is concerned with the problem of determining the typical features of a curve when it is observed with noise. It has been shown that one can characterize the Lipschitz singularities of a signal by following the propagation across scales of the modulus maxima of its continuous wavelet transform. A nonparametric approach, based on appropriate thresholding of the empirical wavelet coefficients, is proposed to estimate the wavelet maxima of a signal observed with noise at various scales. In order to identify the singularities of the unknown signal, we introduce a new tool, "the structural intensity", that computes the "density" of the location of the modulus maxima of a wavelet representation along various scales. This approach is shown to be an effective technique for detecting the significant singularities of a signal corrupted by noise and for removing spurious estimates. The asymptotic properties of the resulting estimators are studied and illustrated by simulations. An application to a real data set is also proposed
Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems
This paper deals with the resolution of inverse problems in a periodic
setting or, in other terms, the reconstruction of periodic continuous-domain
signals from their noisy measurements. We focus on two reconstruction
paradigms: variational and statistical. In the variational approach, the
reconstructed signal is solution to an optimization problem that establishes a
tradeoff between fidelity to the data and smoothness conditions via a quadratic
regularization associated to a linear operator. In the statistical approach,
the signal is modeled as a stationary random process defined from a Gaussian
white noise and a whitening operator; one then looks for the optimal estimator
in the mean-square sense. We give a generic form of the reconstructed signals
for both approaches, allowing for a rigorous comparison of the two.We fully
characterize the conditions under which the two formulations yield the same
solution, which is a periodic spline in the case of sampling measurements. We
also show that this equivalence between the two approaches remains valid on
simulations for a broad class of problems. This extends the practical range of
applicability of the variational method
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