Related papers: Non-commutative time-frequency tomography
Phase-space analysis or time-frequency analysis can be thought as Fourier analysis simultaneously both in time and in frequency, originating from signal processing and quantum mechanics. On groups having unitary Fourier transform, we…
In modelling time series data coming from different sources, frequencies can easily vary since some variable can be measured at higher frequencies, others, at lower frequencies. Given data measured over spatial units and at varying…
The short-time Fourier transform (STFT) represents a window of audio samples as a set of complex coefficients. These are advantageously viewed as magnitudes and phases and the overall distribution of phases is very often assumed to be…
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
We address the problem of estimating time and frequency shifts of a known waveform in the presence of multiple measurement vectors (MMVs). This problem naturally arises in radar imaging and wireless communications. Specifically, a signal…
In audio signal processing, probabilistic time-frequency models have many benefits over their non-probabilistic counterparts. They adapt to the incoming signal, quantify uncertainty, and measure correlation between the signal's amplitude…
Recent experiments have demonstrated that it is possible to alter the dispersion of a medium without significantly altering its absorption or refractive index and that this may be done while a wave propagates through the medium. This…
This paper addresses the problem of efficiently jointly representing a non-stationary multicomponent signal in time and frequency. We introduce a novel enhancement of the time-reassigned synchrosqueezing method designed to compute sharpened…
The spectral distribution $f(\omega)$ of a stationary time series $\{Y_t\}_{t\in\mathbb{Z}}$ can be used to investigate whether or not periodic structures are present in $\{Y_t\}_{t\in\mathbb{Z}}$, but $f(\omega)$ has some limitations due…
A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called harmonic Gaussian…
Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments of the field to be…
This work investigates the effects of time-varying media, where optical properties change over time, on electromagnetic wave propagation, focusing on plane waves and free-electron evanescent waves. We introduce a switching parameter,…
Many real-life signals, such as gravitational wave measurements, biomedical signals, or geophysical data, are strongly non-stationary but can be decomposed into mono-component signals that contain only one active frequency over time. This…
The generalizations of instantaneous frequency and instantaneous bandwidth to a bivariate signal are derived. These are uniquely defined whether the signal is represented as a pair of real-valued signals, or as one analytic and one…
Wave propagation in time-varying media enables unique control of energy transport by breaking energy conservation through temporal modulation. Among the resulting phenomena, temporal disorder-random fluctuations in material parameters-can…
Most data processing techniques, applied to biomedical and sociological time series, are only valid for random fluctuations that are stationary in time. Unfortunately, these data are often non stationary and the use of techniques of…
Given a heterogeneous time-series sample, the objective is to find points in time (called change points) where the probability distribution generating the data has changed. The data are assumed to have been generated by arbitrary unknown…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…
In this paper, the instantaneous frequency estimation of nonstationary signals is considered. The instantaneous frequency is estimated from the timefrequency representation where certain percent of the coefficients is missing. The…