Related papers: Time-frequency analysis on flat tori and Gabor fra…
While spike trains are obviously not band-limited, the theory of super-resolution tells us that perfect recovery of unknown spike locations and weights from low-pass Fourier transform measurements is possible provided that the minimum…
Synchrosqueezing transform (SST) is a useful tool for vibration signal analysis due to its high time-frequency (TF) concentration and reconstruction properties. However, existing SST requires much processing time for large-scale data. In…
The transfer matrix of scattering theory in one dimension can be expressed in terms of the time-evolution operator for an effective non-unitary quantum system. In particular, it admits a Dyson series expansion which turns out to facilitate…
Graph signal processing (GSP) facilitates the analysis of high-dimensional data on non-Euclidean domains by utilizing graph signals defined on graph vertices. In addition to static data, each vertex can provide continuous time-series…
The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz…
Given a non-quasianalytic subadditive weight function $\omega$ we consider the weighted Schwartz space $\mathcal{S}_\omega$ and the short-time Fourier transform on $\mathcal{S}_\omega$, $\mathcal{S}'_\omega$ and on the related modulation…
In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best $s$-term approximation of the Discrete Fourier Transform (DFT) $\mathbf{\hat{f}} \in \mathbb{C}^N$ of any given input vector…
Contradictory theoretical results for oxygen vacancies in SrTiO$_3$ (STO) were often related to the peculiar properties of STO, which is a $d^0$ transition metal oxide with mixed ionic-covalent bonding. Here, we apply, for the first time,…
Time-frequency analysis, such as the Gabor transform, plays an important role in many signal processing applications. The redundancy of such representations is often directly related to the computational load of any algorithm operating in…
We prove that the short-time Fourier transform with Gaussian window performs $L^2$-local stable phase retrieval at the constant function. The proof involved significant interplay between mathematicians and LLMs. An autoformalization in Lean…
The covariance function and the variogram play very important roles in modelling and in prediction of spatial and spatio-temporal data. The assumption of second order stationarity, in space and time, is often made in the analysis of spatial…
In this paper, we extend the quadratic phase Fourier transform of a complex valued functions to that of the quaternion valued functions of two variables. We call it the quaternion quadratic phase Fourier transform (QQPFT). Based on the…
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…
We introduce a numerical method for the solution of the time-dependent Schrodinger equation with a smooth potential, based on its reformulation as a Volterra integral equation. We present versions of the method both for periodic boundary…
Exploring the concept of the extended Galilei group $\mathcal{G}$, a representation for the symplectic quantum mechanics in the manifold of $\mathcal{G}$, written in the light-cone of a five-dimensional De Sitter space-time, is derived…
This article introduces the Generalized Fourier Series (GFS), a novel spectral method that extends the clas- sical Fourier series to non-periodic functions. GFS addresses key challenges such as the Gibbs phenomenon and poor convergence in…
In this paper, we propose the Fourier frequency vector (FFV), inherently, associated with multidimensional Fourier transform. With the help of FFV, we are able to provide physical meaning of so called negative frequencies in…
Fourier transform spectroscopy (FTS) has been widely used in a variety of fields in research, industry, and medicine due to its high signal-to-noise ratio, simultaneous acquisition of signals in a broad spectrum, and versatility for…
Audio signal processing frequently requires time-frequency representations and in many applications, a non-linear spacing of frequency-bands is preferable. This paper introduces a framework for efficient implementation of invertible signal…
In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform (NFT). In particular, we provide…