2,798 research outputs found
Non-Gaussian statistics in space plasma turbulence, fractal properties and pitfalls
Magnetic field fluctuations in the vicinity of the Earth's bow shock have
been investigated with the aim to characterize the intermittent behaviour of
strong plasma turbulence. The observed small-scale intermittency may be the
signature of a multifractal process but a deeper inspection reveals caveats in
such an interpretation. Several effects, including the anisotropy of the
wavefield, the violation of the Taylor hypothesis and the occasional occurrence
of coherent wave packets, strongly affect the higher order statistical
properties. After correcting these effects, a more Gaussian and scale-invariant
wavefield is recovered.Comment: 13 pages (including 13 postscript figures), to appear in Nonlinear
Processes in Geophysic
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
Simulation of Gegenbauer Processes using Wavelet Packets
In this paper, we study the synthesis of Gegenbauer processes using the
wavelet packets transform. In order to simulate a 1-factor Gegenbauer process,
we introduce an original algorithm, inspired by the one proposed by Coifman and
Wickerhauser [1], to adaptively search for the best-ortho-basis in the wavelet
packet library where the covariance matrix of the transformed process is nearly
diagonal. Our method clearly outperforms the one recently proposed by [2], is
very fast, does not depend on the wavelet choice, and is not very sensitive to
the length of the time series. From these first results we propose an algorithm
to build bases to simulate k-factor Gegenbauer processes. Given its practical
simplicity, we feel the general practitioner will be attracted to our
simulator. Finally we evaluate the approximation due to the fact that we
consider the wavelet packet coefficients as uncorrelated. An empirical study is
carried out which supports our results
Hyperspectral image compression : adapting SPIHT and EZW to Anisotropic 3-D Wavelet Coding
Hyperspectral images present some specific characteristics that should be used by an efficient compression system. In compression, wavelets have shown a good adaptability to a wide range of data, while being of reasonable complexity. Some wavelet-based compression algorithms have been successfully used for some hyperspectral space missions. This paper focuses on the optimization of a full wavelet compression system for hyperspectral images. Each step of the compression algorithm is studied and optimized. First, an algorithm to find the optimal 3-D wavelet decomposition in a rate-distortion sense is defined. Then, it is shown that a specific fixed decomposition has almost the same performance, while being more useful in terms of complexity issues. It is shown that this decomposition significantly improves the classical isotropic decomposition. One of the most useful properties of this fixed decomposition is that it allows the use of zero tree algorithms. Various tree structures, creating a relationship between coefficients, are compared. Two efficient compression methods based on zerotree coding (EZW and SPIHT) are adapted on this near-optimal decomposition with the best tree structure found. Performances are compared with the adaptation of JPEG 2000 for hyperspectral images on six different areas presenting different statistical properties
Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multi-wavelets
A new time-varying autoregressive (TVAR) modelling approach is proposed for nonstationary signal processing and analysis, with application to EEG data modelling and power spectral estimation. In the new parametric modelling framework, the time-dependent coefficients of the TVAR model are represented using a novel multi-wavelet decomposition scheme. The time-varying modelling problem is then reduced to regression selection and parameter estimation, which can be effectively resolved by using a forward orthogonal regression algorithm. Two examples, one for an artificial signal and another for an EEG signal, are given to show the effectiveness and applicability of the new TVAR modelling method
Synchrosqueezed Wave Packet Transforms and Diffeomorphism Based Spectral Analysis for 1D General Mode Decompositions
This paper develops new theory and algorithms for 1D general mode
decompositions. First, we introduce the 1D synchrosqueezed wave packet
transform and prove that it is able to estimate the instantaneous information
of well-separated modes from their superposition accurately. The
synchrosqueezed wave packet transform has a better resolution than the
synchrosqueezed wavelet transform in the time-frequency domain for separating
high frequency modes. Second, we present a new approach based on
diffeomorphisms for the spectral analysis of general shape functions. These two
methods lead to a framework for general mode decompositions under a weak
well-separation condition and a well different condition. Numerical examples of
synthetic and real data are provided to demonstrate the fruitful applications
of these methods.Comment: 39 page
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
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