Related papers: Sampling time-frequency localized functions and co…
In this article, we present a space-frequency theory for spherical harmonics based on the spectral decomposition of a particular space-frequency operator. The presented theory is closely linked to the theory of ultraspherical polynomials on…
We present a novel family of continuous, linear time-frequency transforms adaptable to a multitude of (nonlinear) frequency scales. Similar to classical time-frequency or time-scale representations, the representation coefficients are…
Describing a time series parsimoniously is the first step to study the underlying dynamics. For a time-discrete system, a generating partition provides a compact description such that a time series and a symbolic sequence are one-to-one.…
This paper presents an application of time-frequency methods to characterize the dispersion of acoustic waves travelling in a one-dimensional periodic or disordered lattice made up of Helmholtz resonators connected to a cylindrical tube.…
Time-frequency localization operators, originally introduced by Daubechies (1988), provide a framework for localizing signals in the phase space and have become a central tool in time-frequency analysis. In this paper we introduce and study…
A warping operator consists of an invertible axis deformation applied either in the signal domain or in the corresponding Fourier domain. Additionally, a warping transformation is usually required to preserve the signal energy, thus…
Localized vibrations, arising from nonlinearities or symmetry breaking, pose a challenge in engineering, as the resulting high-amplitude vibrations may result in component failure due to fatigue. During operation, the emergence of…
We propose a new information aggregation method which called Localized Feature Aggregation Module based on the similarity between the feature maps of an encoder and a decoder. The proposed method recovers positional information by…
This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…
Phase clocks are synchronization tools that implement a form of logical time in distributed systems. For systems tolerating transient faults by self-repair of damaged data, phase clocks can enable reasoning about the progress of distributed…
The frame set of a function $g\in L^2(\mathbb{R})$ is the subset of all parameters $(a, b)\in \mathbb{R}^2_+$ for which the time-frequency shifts of $g$ along $a\mathbb{Z}\times b\mathbb{Z}$ form a Gabor frame for $L^2(\mathbb{R}).$ In this…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
This paper considers the problem of sampling and reconstruction of a continuous-time sparse signal without assuming the knowledge of the sampling instants or the sampling rate. This topic has its roots in the problem of recovering multiple…
This paper investigates homogenization problems for the nonlocal operators with rapidly oscillating coefficients in the cases of periodic and random statistically homogeneous micro-structures. These operators involve the fractional…
Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply…
This paper develops an algorithmic framework for tracking fixed points of time-varying contraction mappings. Analytical results for the tracking error are established for the cases where: (i) the underlying contraction self-map changes at…
This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time, while…
In this paper we construct frames of Gabor type for the space $L^2_{rad}(\R^d)$ of radial $L^2$-functions, and more generally, for subspaces of modulation spaces consisting of radial distributions. Hereby, each frame element itself is a…
Adaptivity and local mesh refinement are crucial for the efficient numerical simulation of wave phenomena in complex geometry. Local mesh refinement, however, can impose a tiny time-step across the entire computational domain when using…
The Mixed Lebesgue space is a suitable tool for modelling and measuring signals living in time-space domains. And sampling in such spaces plays an important role for processing high-dimensional time-varying signals. In this paper, we first…