Related papers: Balayage and Short time Fourier transform frames
Unsupervised/self-supervised time series representation learning is a challenging problem because of its complex dynamics and sparse annotations. Existing works mainly adopt the framework of contrastive learning with the time-based…
The Heisenberg time-energy relation prevents determination of an atomic transition to better than the inverse of the measurement time. The relation generally applies to frequency estimation of a near-resonant field [1-3], since information…
Numerical simulation of Fresnel diffraction with fast Fourier transform (FFT) is widely used in optics, especially computer holography. Fresnel diffraction with FFT cannot set different sampling rates between source and destination planes,…
We define ultradistributional wave front sets with respect to translation-modulation invariant Banach spaces of ultradistributions having solid Fourier image. The main result is their characterisation by the short-time Fourier transform.
Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three-dimensional truncated Fourier series at a set of…
Temporal alignment of multiple signals through time warping is crucial in many fields, such as classification within speech recognition or robot motion learning. Almost all related works are limited to data in Euclidean space. Although an…
The problem of approximately computing the $k$ dominant Fourier coefficients of a vector $X$ quickly, and using few samples in time domain, is known as the Sparse Fourier Transform (sparse FFT) problem. A long line of work on the sparse FFT…
Resonance frequencies can provide useful information on the deformation occurring during fracturing experiments or $CO_2$ management, complementary to the microseismic event distribution. An accurate time-frequency representation is of…
We consider a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to Fourier synthesis. It refines previous contributions, in which the preprocessing of…
We present a modified Front Tracking (mFT) scheme for hyperbolic systems of conservation laws in one space dimension, in which we allow arbitrarily large nonlinear waves. We build the scheme by introducing and solving a ``generalized…
By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.
Ballistic Macroscopic Fluctuation Theory (BMFT) captures the evolution of fluctuations and correlations in systems where transport is strictly ballistic. We show that, for \emph{generic integrable models}, BMFT can be constructed through a…
The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic…
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…
The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection $A$ on a line bundle $L$ and a section $\phi$ of another…
We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe.…
A transition of focus from state space to frames of reference and their transformations is argued as being the appropriate setup for ensuring the covariance of physical laws. Such an approach can not only simplify and clarify aspects of…
One of the major challenges of employing a dual-frequency phase-shifting algorithm for phase retrieval is its sensitivity to noise. Yun et. al [H Yun, B Li, S Zhang. 2017] proposed a dual-frequency method based on the Fourier transform…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…
A sharper uncertainty inequality which exhibits a lower bound larger than that in the classical N-dimensional Heisenberg's uncertainty principle is obtained, and extended from N-dimensional Fourier transform domain to two N-dimensional…