Related papers: More Uncertainty Principles for Metaplectic Time-F…
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…
Recent developments in machine learning and signal processing have resulted in many new techniques that are able to effectively capture the intrinsic yet complex properties of hyperspectral imagery. Tasks ranging from anomaly detection to…
The paper studies properties of continuous time processes with spectrum degeneracy at a single point where their Fourier transforms vanish with a certain rate. It appears that these processes are linearly predictable in some weak sense,…
Many astrophysical phenomena are time-varying, in the sense that their brightness change over time. In the case of periodic stars, previous approaches assumed that changes in period, amplitude, and phase are well described by either…
We use spectral projections of time operator in the Liouville space for simple quantum scattering systems in order to define a space of unstable particle states evolving under a contractive semi-group. This space includes purely…
In the field of applied mathematics the Fourier transform has developed into an important tool. It is a powerful method for solving partial differential equations. The Fourier transform provides also a technique for signal analysis where…
In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence of bounded electric and magnetic potentials. Under suitable…
Time-frequency representations stemmed in 1932 with the introduction of the Wigner distribution. For most of the 20th century, research in this area primarily focused on defining joint probability distributions for position and momentum in…
This work considers uncertainty relations on time frequency distributions from a signal processing viewpoint. An uncertainty relation on the marginalizable time frequency distributions is given. A result from quantum mechanics is used on…
We show various uncertainty principles for the Fourier transform on harmonic manifolds of rank one. In particular, we derive a Heisenberg uncertainty principle, a Morgen theorem, an uncertainty principle for the Schr\"odinger equation and a…
Inverse Uncertainty Quantification (IUQ) method has been widely used to quantify the uncertainty of Physical Model Parameters (PMPs) in nuclear Thermal Hydraulics (TH) systems. This paper introduces a novel hierarchical Bayesian model which…
Metaplectic Wigner distributions were recently investigated as natural generalizations of the classical Wigner distribution, and provide a wide class of time-frequency representations that exploits the structure of the symplectic group.…
We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the…
There is a lack of methodological results for continuous time change detection due to the challenges of noninformative prior specification and efficient posterior inference in this setting. Most methodologies to date assume data are…
The Fourier spectral techniques that are common in Astronomy for analyzing periodic or multi-periodic light-curves lose their usefulness when they are applied to unsteady light-curves. We review some of the novel techniques that have been…
In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the Clifford-Fourier transform on $\mathbb{R}^m$.
We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by…
The short-time Fourier transform (STFT) is widely used for analyzing non-stationary signals. However, its performance is highly sensitive to its parameters, and manual or heuristic tuning often yields suboptimal results. To overcome this…
The advent of novel nonlinear materials has stirred unprecedented interest in exploring the use of temporal inhomogeneities to achieve novel forms of wave control, amidst the greater vision of engineering metamaterials across both space and…
Quantum group Fourier transform methods are applied to the study of processes on noncommutative Minkowski spacetime $[x^i,t]=\imath\lambda x^i$. A natural wave equation is derived and the associated phenomena of {\it in vacuo} dispersion…