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We introduce new frames, called \textit{metaplectic Gabor frames}, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions. Namely, we develop the theory of metaplectic atoms in a full-general setting…

Analysis of PDEs · Mathematics 2024-01-18 Elena Cordero , Gianluca Giacchi

In digital signal processing time-frequency transforms are used to analyze time-varying signals with respect to their spectral contents over time. Apart from the commonly used short-time Fourier transform, other methods exist in literature,…

Signal Processing · Electrical Eng. & Systems 2021-01-19 Stefan Scholl

In time series classification and regression, signals are typically mapped into some intermediate representation used for constructing models. Since the underlying task is often insensitive to time shifts, these representations are required…

Sound · Computer Science 2019-07-16 Joakim Andén , Vincent Lostanlen , Stéphane Mallat

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…

Classical Analysis and ODEs · Mathematics 2019-03-14 M. El Kassimi , S. Fahlaoui

We study extra time-frequency shift invariance properties of Gabor spaces. For a Gabor space generated by an integer lattice, we state and prove several characterizations for its time-frequency shift invariance with respect to a finer…

Classical Analysis and ODEs · Mathematics 2017-11-07 Carlos Cabrelli , Dae Gwan Lee , Ursula Molter , Goetz E. Pfander

New definitions are suggested for frequencies which may be instantaneous or not. The Heisenberg-Gabor inequality and the Shannon sampling theorem are briefly discussed.

Computational Engineering, Finance, and Science · Computer Science 2007-05-23 Michel Fliess

We develop a theory of quantum harmonic analysis on lattices in $\mathbb{R}^{2d}$. Convolutions of a sequence with an operator and of two operators are defined over a lattice, and using corresponding Fourier transforms of sequences and…

Functional Analysis · Mathematics 2020-05-11 Eirik Skrettingland

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 area of Fourier analysis connected to signal processing theory has undergone a rapid development in the last two decades. The aspect of this development that has received the most publicity is the theory of wavelets and their relatives,…

Classical Analysis and ODEs · Mathematics 2007-05-23 G B Folland

The problem of joint estimation of power spectrum and modulation from realizations of frequency modulated stationary wideband signals is considered. The study is motivated by some specific signal classes from which departures to…

Statistics Theory · Mathematics 2013-05-15 Harold Omer , Bruno Torrésani

The "theoretical limit of time-frequency resolution in Fourier analysis" is thought to originate in certain mathematical and/or physical limitations. This, however, is not true. The actual origin arises from the numerical (technical) method…

Physics and Society · Physics 2025-03-28 Fumihiko Ishiyama

The topic of this paper are (multi-window) Gabor frames for signals over finite Abelian groups, generated by an arbitrary lattice within the finite time-frequency plane. Our generic approach covers simultaneously multi-dimensional signals…

Group Theory · Mathematics 2008-03-17 H. G. Feichtinger , W. Kozek , F. Luef

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…

Classical Analysis and ODEs · Mathematics 2019-01-07 Mohammed El Kassimi , Mustapha Boujeddaine , Said Fahlaoui

We establish a direct link between the time-reversal technique and the so-called adjoint method for imaging. Using this relationship, we derive new solution strategies for an inverse problem which arises in telecommunication. These…

Optimization and Control · Mathematics 2007-05-23 Oliver Dorn

We extend the Gabor analysis in \cite{GaSa} to a broad class of modulation spaces, allowing more general mixed quasi-norm estimates and weights in the definition of the modulation space quasi-norm. For such spaces we deduce invariance and…

Functional Analysis · Mathematics 2014-09-09 Joachim Toft

We study functions whose time-frequency content are concentrated in a compact region in phase space using time-frequency localization operators as a main tool. We obtain approximation inequalities for such functions using a finite linear…

Functional Analysis · Mathematics 2016-12-28 Monika Dörfler , Gino Angelo Velasco

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,…

Data Analysis, Statistics and Probability · Physics 2008-07-23 Carsten Allefeld

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…

Classical Analysis and ODEs · Mathematics 2020-11-03 Andrew Ahn , William Clark , Shahaf Nitzan , Joseph Sullivan

A general rate theory for resonance energy transfer is formulated to incorporate any degrees of freedom (e.g., rotation, vibration, exciton, and polariton) as well as coherently-coupled composite states. The compact rate expression allows…

Chemical Physics · Physics 2022-01-31 Jianshu Cao

A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…

Chemical Physics · Physics 2007-05-23 V. V. Ryazanov