4,528 research outputs found
Spectral analysis of stationary random bivariate signals
A novel approach towards the spectral analysis of stationary random bivariate
signals is proposed. Using the Quaternion Fourier Transform, we introduce a
quaternion-valued spectral representation of random bivariate signals seen as
complex-valued sequences. This makes possible the definition of a scalar
quaternion-valued spectral density for bivariate signals. This spectral density
can be meaningfully interpreted in terms of frequency-dependent polarization
attributes. A natural decomposition of any random bivariate signal in terms of
unpolarized and polarized components is introduced. Nonparametric spectral
density estimation is investigated, and we introduce the polarization
periodogram of a random bivariate signal. Numerical experiments support our
theoretical analysis, illustrating the relevance of the approach on synthetic
data.Comment: 11 pages, 3 figure
Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals
There are three equivalent ways of representing two jointly observed
real-valued signals: as a bivariate vector signal, as a single complex-valued
signal, or as two analytic signals known as the rotary components. Each
representation has unique advantages depending on the system of interest and
the application goals. In this paper we provide a joint framework for all three
representations in the context of frequency-domain stochastic modeling. This
framework allows us to extend many established statistical procedures for
bivariate vector time series to complex-valued and rotary representations.
These include procedures for parametrically modeling signal coherence,
estimating model parameters using the Whittle likelihood, performing
semi-parametric modeling, and choosing between classes of nested models using
model choice. We also provide a new method of testing for impropriety in
complex-valued signals, which tests for noncircular or anisotropic second-order
statistical structure when the signal is represented in the complex plane.
Finally, we demonstrate the usefulness of our methodology in capturing the
anisotropic structure of signals observed from fluid dynamic simulations of
turbulence.Comment: To appear in IEEE Transactions on Signal Processin
Bivariate phase-rectified signal averaging
Phase-Rectified Signal Averaging (PRSA) was shown to be a powerful tool for
the study of quasi-periodic oscillations and nonlinear effects in
non-stationary signals. Here we present a bivariate PRSA technique for the
study of the inter-relationship between two simultaneous data recordings. Its
performance is compared with traditional cross-correlation analysis, which,
however, does not work well for non-stationary data and cannot distinguish the
coupling directions in complex nonlinear situations. We show that bivariate
PRSA allows the analysis of events in one signal at times where the other
signal is in a certain phase or state; it is stable in the presence of noise
and impassible to non-stationarities.Comment: 19 pages, 6 figures, revised version submitted to Physica
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
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