Related papers: Time-Varying Spectrum of the Random String

The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the…

We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem.…

We describe here an experimental technique based on the acoustic scattering phenomenon allowing the direct probing of the vorticity field in a turbulent flow. Using time-frequency distributions, recently introduced in signal analysis…

We address the problem of finding star algebra projectors that exhibit localized time profiles. We use the double Wick rotation method, starting from an Euclidean (unconventional) lump solution, which is characterized by the Neumann matrix…

In this paper, we deal with the inverse source problem of determining a source in a time fractional diffusion equation where data are given at a fixed time. This problem is ill-posed, i.e., the solution does not depend continuously on the…

A new algorithm for estimating the time-varying frequency of a noiseless sinusoidal signal is considered. It is assumed that the amplitude and frequency of the sinusoidal signal are unknown functions of time, but are solutions of linear…

The time dependence of quantum evanescent waves generated by a point source with an infinite or a limited frequency band is analyzed. The evanescent wave is characterized by a forerunner (transient) related to the precise way the source is…

In this paper, we study the decoherence of a wave described by the solution to a Schroedinger equation with a time-dependent random potential. The random potential is assumed to have slowly decaying correlations. The main tool to analyze…

There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often…

We examine the possibility that time dependence might remove the singular nature of global string spacetimes. We first show that this time dependence takes a specific form -- a de-Sitter like expansion along the length of the string and…

This paper is a contribution to the old problem of representing a signal in the coordinates of time and frequency. As the starting point, we abandon Gabor's complex extension and re-evaluate fundamental principles of time-frequency…

Tracking the solution of time-varying variational inequalities is an important problem with applications in game theory, optimization, and machine learning. Existing work considers time-varying games or time-varying optimization problems.…

A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear…

This paper develops change-point methods for the spectrum of a locally stationary time series. We focus on series with a bounded spectral density that change smoothly under the null hypothesis but exhibits change-points or becomes less…

We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…

We derive the asymptotic distribution of the null spectrum of the well-known Multiple Signal Classification (MUSIC) in its computational Time-Reversal (TR) form. The result pertains to a single-frequency non-colocated multistatic scenario…

We consider non-stationary oscillations of an infinite string with time-varying tension. The string lies on the Winkler foundation with a point inhomogeneity (a concentrated spring of negative stiffness). In such a system with constant…

We study the problem of estimating time-varying coefficients in ordinary differential equations. Current theory only applies to the case when the associated state variables are observed without measurement errors as presented in…

In this letter, based on the variational model, we propose a novel time-frequency post-processing technique to approximate the ideal time-frequency representation. Our method has the advantage of modularity, enabling "plug and play",…

A phenomenological model describing the time-frequency dependence of the power spectrum of thin plates vibrating in a wave turbulence regime, is introduced. The model equation contains as basic solutions the Rayleigh-Jeans equipartition of…