2,549,885 research outputs found
Application of the Hilbert-Huang Transform to the Search for Gravitational Waves
We present the application of a novel method of time-series analysis, the
Hilbert-Huang Transform, to the search for gravitational waves. This algorithm
is adaptive and does not impose a basis set on the data, and thus the
time-frequency decomposition it provides is not limited by time-frequency
uncertainty spreading. Because of its high time-frequency resolution it has
important applications to both signal detection and instrumental
characterization. Applications to the data analysis of the ground and space
based gravitational wave detectors, LIGO and LISA, are described
The Synchrosqueezing transform for instantaneous spectral analysis
The Synchrosqueezing transform is a time-frequency analysis method that can
decompose complex signals into time-varying oscillatory components. It is a
form of time-frequency reassignment that is both sparse and invertible,
allowing for the recovery of the signal. This article presents an overview of
the theory and stability properties of Synchrosqueezing, as well as
applications of the technique to topics in cardiology, climate science and
economics
Analysis of Modulated Multivariate Oscillations
The concept of a common modulated oscillation spanning multiple time series
is formalized, a method for the recovery of such a signal from potentially
noisy observations is proposed, and the time-varying bias properties of the
recovery method are derived. The method, an extension of wavelet ridge analysis
to the multivariate case, identifies the common oscillation by seeking, at each
point in time, a frequency for which a bandpassed version of the signal obtains
a local maximum in power. The lowest-order bias is shown to involve a quantity,
termed the instantaneous curvature, which measures the strength of local
quadratic modulation of the signal after demodulation by the common oscillation
frequency. The bias can be made to be small if the analysis filter, or wavelet,
can be chosen such that the signal's instantaneous curvature changes little
over the filter time scale. An application is presented to the detection of
vortex motions in a set of freely-drifting oceanographic instruments tracking
the ocean currents
Determination of fundamental asteroseismic parameters using the Hilbert transform
Context. Solar-like oscillations exhibit a regular pattern of frequencies.
This pattern is dominated by the small and large frequency separations between
modes. The accurate determination of these parameters is of great interest,
because they give information about e.g. the evolutionary state and the mass of
a star.
Aims. We want to develop a robust method to determine the large and small
frequency separations for time series with low signal-tonoise ratio. For this
purpose, we analyse a time series of the Sun from the GOLF instrument aboard
SOHO and a time series of the star KIC 5184732 from the NASA Kepler satellite
by employing a combination of Fourier and Hilbert transform.
Methods. We use the analytic signal of filtered stellar oscillation time
series to compute the signal envelope. Spectral analysis of the signal envelope
then reveals frequency differences of dominant modes in the periodogram of the
stellar time series.
Results. With the described method the large frequency separation
can be extracted from the envelope spectrum even for data of poor
signal-to-noise ratio. A modification of the method allows for an overview of
the regularities in the periodogram of the time series.Comment: 7 pages, 7 figures, 2 tables, submitted to A&
A new statistical test based on the wavelet cross-spectrum to detect time–frequency dependence between non-stationary signals: Application to the analysis of cortico-muscular interactions
The study of the correlations that may exist between neurophysiological signals is at the heart of modern techniques for data analysis in neuroscience. Wavelet coherence is a popular method to construct a time-frequency map that can be used to analyze the time-frequency correlations be- tween two time series. Coherence is a normalized measure of dependence, for which it is possible to construct confidence intervals, and that is commonly considered as being more interpretable than the wavelet cross-spectrum (WCS). In this paper, we provide empirical and theoretical arguments to show that a significant level of wavelet coherence does not necessarily correspond to a significant level of dependence between random signals, especially when the number of trials is small. In such cases, we demonstrate that the WCS is a much better measure of statistical dependence, and a new statistical test to detect significant values of the cross-spectrum is proposed. This test clearly outperforms the limitations of coherence analysis while still allowing a consistent estimation of the time-frequency correlations between two non-stationary stochastic processes. Simulated data are used to investigate the advantages of this new approach over coherence analysis. The method is also applied to experimental data sets to analyze the time-frequency correlations that may exist between electroencephalogram (EEG) and surface electromyogram (EMG)
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