Related papers: Bicoherence analysis of nonstationary and nonlinea…
Deriving meaningful information from observational data is often restricted by many limiting factors, the most important of which is the presence of noise. In this work, we present the use of the bicoherence function to extract information…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
Noise in various interferometer systems can sometimes couple non-linearly to create excess noise in the gravitational wave (GW) strain data. Third-order statistics, such as bicoherence and biphase, can identify these couplings and help…
Power system coherency refers to the phenomenon that machines in a power network exhibit similar frequency responses after disturbances, and is foundational for model reduction and control design. Despite abundant empirical observations,…
Results are presented from numerical modeling of the effect of the inhomogeneity of the ion background on the complicated spatiotemporal dynamics of an electron beam with a virtual cathode in plane geometry. The possibility is demonstrated…
Cyclic spectral analysis is a signal processing technique designed to deal with stochastic signals whose statistics vary periodically with time. Pulsar radio emission is a textbook example of this signal class, known as cyclostationary…
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…
We present a spectrogram separation method tailored for mixtures comprising two nonstationary components. By exploiting the unique characteristics of their time-frequency representations, we propose an inverse problem formulation to…
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…
Higher-order spectra (or polyspectra), defined as the Fourier Transform of a stationary process' autocumulants, are useful in the analysis of nonlinear and non Gaussian processes. Polyspectral means are weighted averages over Fourier…
The entrainment between weakly-coupled nonlinear oscillators, as well as between complex signals such as those representing physiological activity, is frequently assessed in terms of whether a stable relationship is detectable between the…
The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article,…
Coherence is a basic phenomenon in quantum mechanics and considered to be an essential resource in quantum information processing. Although the quantification of coherence has attracted a lot of interest, the lack of efficient methods to…
Incoherent noise is manifest in measurements of expectation values when the underlying ensemble evolves under a classical distribution of unitary processes. While many incoherent processes appear decoherent, there are important differences.…
The decoherence rate is a nonlinear channel parameter that describes quantitatively the decay of the off-diagonal elements of a density operator in the decoherence basis. We address the question of how to experimentally access such a…
Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modelled as a distribution of unitary processes arising from slowly…
We focus on an alignment-free method to estimate the underlying signal from a large number of noisy randomly shifted observations. Specifically, we estimate the mean, power spectrum, and bispectrum of the signal from the observations. Since…
Harmonic analysis has provided powerful tools to accurately determine the tune from turn-by-turn data originating from numerical simulations or beam measurements in circular accelerators and storage rings. Methods that have been developed…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
Cross-spectral analysis is a mathematical tool for extracting the power spectral density of a correlated signal from two time series in the presence of uncorrelated interfering signals. We demonstrate and explain a set of conditions where…