Related papers: An invitation to Gabor analysis
This article studies effective communication, one of the three forms identified by Weaver and Shannon, as an enabler for the upcoming 6G use cases. The envisioned tactile, holographic, and multi-sensory communications require bandwidths in…
We apply a new approach to the study of the density of Gabor systems, and obtain a simple and straightforward proof of Ramanathan and Steger's well known result regarding the density of Gabor frames and Gabor Riesz sequences. Moreover, this…
Long ago appeared a discussion in quantum mechanics of the problem of opening a completely absorbing shutter on which were impinging a stream of particles of definite velocity. The solution of the problem was obtained in a form entirely…
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years,…
Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in…
Wireless communications in the terahertz band have been recently proposed as complement to conventional wired interconnects within computing packages. Such environments are typically highly reverberant, hence showing long channel impulse…
The odds theorem and the corresponding solution algorithm (odds algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have caught much attention. (Google for instance "Bruss odds" to obtain…
One of the most remarkable predictions to emerge out of the exact infinite-dimensional solution of the glass problem is the Gardner transition. Although this transition was first theoretically proposed a generation ago for certain…
We use time-frequency methods for the study of Fourier Integral operators (FIOs). In this paper we shall show that Gabor frames provide very efficient representations for a large class of FIOs. Indeed, similarly to the case of shearlets and…
This paper introduces Gabor scattering, a feature extractor based on Gabor frames and Mallat's scattering transform. By using a simple signal model for audio signals specific properties of Gabor scattering are studied. It is shown that for…
We study the Wigner kernel and the Gabor matrix associated with the propagators of a broad class of linear evolution equations, including the complex heat, wave, and Hermite equations. Within the framework of time-frequency analysis, we…
This article serves as a supplement to the recently published call for participation in a Research Topic [1] that is timed to commemorate the 75th anniversary of Shannon's pioneering 1948 paper [2]. Here, we include some citations of key…
This paper is a contribution to frame theory. Frames in a Hilbert space are generalizations of orthonormal bases. In particular, Gabor frames of $L^2(\mathbb{R})$, which are made of translations and modulations of one or more windows, are…
This text describes a generalization of the analytic signal (Gabor, 1946) approach for the definition of instantaneous amplitude and phase to the case of multivariate signals. It was originally written as an appendix for another paper,…
Not only motivated by the fact that the publication of the GAFT first appeared 60 years ago in print we reconstruct its history and so show that it is no exaggeration to claim that it has appeared already 75 years ago!
We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then…
We study Dirichlet-type problems for the simplest third-order linear dispersive PDE, often referred to as the Airy equation. Such problems have not been extensively studied, perhaps due to the complexity of the spectral structure of the…
We consider Gabor Riesz sequences generated by a lattice $\Lambda \subset \mathbb{R}^2$ and a window function $g \in L^2(\mathbb{R})$ which is well localized in both time and frequency. When $g$ belongs to the Feichtinger algebra, we prove…
This chapter is motivated by the need for a rigorous and comprehensive analysis of the Doppler effects encountered by electromagnetic and acoustic signals across a diverse spectrum of modern applications. These include land mobile…
Practically and intrinsically, inclusions of operator algebras are of fundamental interest. The subject of this paper is intermediate operator algebras of inclusions. There are two previously known theorems which naturally and completely…