Related papers: An introduction to the Gabor wave front set
We present the early release of the atlas of continuous gravitational waves covering frequencies from 20 Hz to 1500 Hz and spindowns from -5e-10 to 5e-10 Hz/s. Compared to the previous atlas release we have greatly expanded the parameter…
The recent announcement of evidence for a stochastic background of gravitational waves (GWB) in pulsar timing array (PTA) data has piqued interest across the scientific community. A combined analysis of all currently available data holds…
Identification of a transient gravitational-wave signal embedded into non-stationary noise requires the analysis of time-dependent spectral components in the resulting time series. The time-frequency distribution of the signal power can be…
By the important applications of Gabor transform in time-frequency analysis and signal analysis, in this paper, we consider the Gabor quaternion Fourier transform (GQFT), and we prove of it a version Benedicks-type uncertainty principle for…
Concepts and formalism from acoustics are often used to exemplify quantum mechanics. Conversely, quantum mechanics could be used to achieve a new perspective on acoustics, as shown by Gabor studies. Here, we focus in particular on the study…
In this article, I present an elementary introduction to the theory of gravitational waves. This article is meant for students who have had an exposure to general relativity, but, results from general relativity used in the main discussion…
In this paper we study propagation of the high frequency electromagnetic waves in a curved spacetime. We discuss a so call spinoptics approach which generalizes a well known geometric optics approximation and allows one to take into account…
We provide a construction of Gabor frames that encode local linearizations of a signal detected on a curved smooth manifold of arbitrary dimension, with Gabor filters that can detect the presence of higher-dimensional boundaries in the…
The Aharonov-Bohm scattering of a localized wave packet is considered. A careful analysis of the forward direction points out new results: according to the time-dependent solution obtained by means of the asymptotic representation for the…
We show the full structure of the frame set for the Gabor system $\mathcal{G}(g;\alpha,\beta):=\{e^{-2\pi i m\beta\cdot}g(\cdot-n\alpha):m,n\in\Bbb Z\}$ with the window being the Haar function $g=-\chi_{[-1/2,0)}+\chi_{[0,1/2)}$. The…
Windowing a Fourier transform is a useful tool, which gives us the similarity between the signal and time frequency signal, and it allows to get sense when/where ceratin frequencies occur in the input signal, this method is introduced by…
An approximate description of surface waves propagating along periodically grooved surfaces is intuitively developed in the limit where the grooves are narrow relative to the period. Considering acoustic and electromagnetic waves guided by…
Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation and spatially inhomogeneous activating agents. We…
We pursue a low-wavenumber, second-order homogenized solution of the time-harmonic wave equation at both low and high frequency in periodic media with a source term whose frequency resides inside a band gap. Considering the wave motion in…
The first focus of this paper is the characterization of the spectrum and the singular values of the coefficient matrix stemming from the discretization with space-time grid for a parabolic diffusion problem and from the approximation of…
A general principle says that the matrix of a Fourier integral operator with respect to wave packets is concentrated near the curve of propagation. We prove a precise version of this principle for Fourier integral operators with a smooth…
Several km-scale gravitational-wave detectors have been constructed world wide. These instruments combine a number of advanced technologies to push the limits of precision length measurement. The core devices are laser interferometers of a…
We use the concept of reproducing pairs to study Gabor systems at critical density. First, we present a generalization of the Balian-Low theorem to the reproducing pairs setting. Then, we prove our main result that there exists a…
A problem of amplitude reconstruction in terms of the given angular distribution is considered. Solution of this problem is not unique. A class of amplitudes, correspondent to one and the same angular distribution, forms a region in…
Recent progress in graph signal processing (GSP) has addressed a number of problems, including sampling and filtering. Proposed methods have focused on generic graphs and defined signals with certain characteristics, e.g., bandlimited…