21,749 research outputs found
Single-trial multiwavelet coherence in application to neurophysiological time series
A method of single-trial coherence analysis is presented, through the application of continuous muldwavelets. Multiwavelets allow the construction of spectra and bivariate statistics such as coherence within single trials. Spectral estimates are made consistent through optimal time-frequency localization and smoothing. The use of multiwavelets is considered along with an alternative single-trial method prevalent in the literature, with the focus being on statistical, interpretive and computational aspects. The multiwavelet approach is shown to possess many desirable properties, including optimal conditioning, statistical descriptions and computational efficiency. The methods. are then applied to bivariate surrogate and neurophysiological data for calibration and comparative study. Neurophysiological data were recorded intracellularly from two spinal motoneurones innervating the posterior,biceps muscle during fictive locomotion in the decerebrated cat
Wavelet transforms and their applications to MHD and plasma turbulence: a review
Wavelet analysis and compression tools are reviewed and different
applications to study MHD and plasma turbulence are presented. We introduce the
continuous and the orthogonal wavelet transform and detail several statistical
diagnostics based on the wavelet coefficients. We then show how to extract
coherent structures out of fully developed turbulent flows using wavelet-based
denoising. Finally some multiscale numerical simulation schemes using wavelets
are described. Several examples for analyzing, compressing and computing one,
two and three dimensional turbulent MHD or plasma flows are presented.Comment: Journal of Plasma Physics, 201
On the Analytic Wavelet Transform
An exact and general expression for the analytic wavelet transform of a
real-valued signal is constructed, resolving the time-dependent effects of
non-negligible amplitude and frequency modulation. The analytic signal is first
locally represented as a modulated oscillation, demodulated by its own
instantaneous frequency, and then Taylor-expanded at each point in time. The
terms in this expansion, called the instantaneous modulation functions, are
time-varying functions which quantify, at increasingly higher orders, the local
departures of the signal from a uniform sinusoidal oscillation. Closed-form
expressions for these functions are found in terms of Bell polynomials and
derivatives of the signal's instantaneous frequency and bandwidth. The analytic
wavelet transform is shown to depend upon the interaction between the signal's
instantaneous modulation functions and frequency-domain derivatives of the
wavelet, inducing a hierarchy of departures of the transform away from a
perfect representation of the signal. The form of these deviation terms
suggests a set of conditions for matching the wavelet properties to suit the
variability of the signal, in which case our expressions simplify considerably.
One may then quantify the time-varying bias associated with signal estimation
via wavelet ridge analysis, and choose wavelets to minimize this bias
The performance of spherical wavelets to detect non-Gaussianity in the CMB sky
We investigate the performance of spherical wavelets in discriminating
between standard inflationary models (Gaussian) and non-Gaussian models. For
the later we consider small perturbations of the Gaussian model in which an
artificially specified skewness or kurtosis is introduced through the Edgeworth
expansion. By combining all the information present in all the wavelet scales
with the Fisher discriminant, we find that the spherical Mexican Hat wavelets
are clearly superior to the spherical Haar wavelets. The former can detect
levels of the skewness and kurtosis of ~1% for 33' resolution, an order of
magnitude smaller than the later. Also, as expected, both wavelets are better
for discriminating between the models than the direct consideration of moments
of the temperature maps. The introduction of instrumental white noise in the
maps, S/N=1, does not change the main results of this paper.Comment: 12 pages, 7 figures, accepted by MNRAS with minor change
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
- …