Related papers: One More Tool for Understanding Resonance
Being a powerful tool for linear time-invariant (LTI) systems, system response analysis can also be applied to the so-called linear space-invariant (LSI) but time-varying systems, which is a dual of the conventional LTI problems. In this…
Temporal sampling does more than add another axis to the vector of observables. Instead, under the recognition that how objects change (and move) in time speaks directly to the physics underlying astronomical phenomena, next-generation…
Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so…
Resonance and decay phenomena are ubiquitous in the quantum world. To understand them in their complexity it is useful to study solvable models in a wide sense, that is, systems which can be treated by analytical means. The present review…
In this paper, a novel time domain sampling method based on the initial arrival time of waves is proposed to reconstruct acoustic sources, including point sources, curve sources, surface sources and block sources. The uniqueness of…
In the last fifteen years, a great progress has been made in the understanding of the nonlinear resonance dynamics of water waves. Notions of scale- and angle-resonances have been introduced, new type of energy cascade due to nonlinear…
Fast camera imaging is used to study ion acoustic waves propagating azimuthally in a magnetized plasma column. The high speed image sequences are analyzed using Proper Orthogonal Decomposition and 2D Fourier Transform, allowing to evaluate…
The wavefront set provides a precise description of the singularities of a distribution. Because of its ability to control the product of distributions, the wavefront set was a key element of recent progress in renormalized quantum field…
Time independent convolution yields circulant matrices whose eigenvectors are the Fourier exponentials with the eigenvalues being the Fourier transform of the mask. The case of time dependent convolution, the non-stationary case, no longer…
Complex spatial dependencies in transportation networks make traffic prediction extremely challenging. Much existing work is devoted to learning dynamic graph structures among sensors, and the strategy of mining spatial dependencies from…
Long term behavior of nonlinear deterministic continuous time signals can be studied in terms of their reconstructed attractors. Reconstructed attractors of a continuous signal are meant to be topologically equivalent representations of the…
In this paper, we study the convolution structure in the special affine Fourier domain to combine the advantages of the well known special affine Fourier and wavelet transforms into a novel integral transform coined as special affine…
This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is…
This report will explore and answer fundamental questions about taking Fourier Transforms and tying it with recent advances in AI and neural architecture. One interpretation of the Fourier Transform is decomposing a signal into its…
The detection of continuous gravitational-wave signals requires to account for the motion of the detector with respect to the solar system barycenter in the data analysis. In order to search efficiently for such signals by means of the fast…
Context. The spatial power spectrum of supergranulation does not fully characterize the underlying physics of turbulent convection. For example, it does not describe the non-Gaussianity in the horizontal flow divergence. Aims. Our aim is to…
Gravitational-wave memory is characterized by a signal component that persists after a transient signal has decayed. Treating such signals in the frequency domain is non-trivial, since discrete Fourier transforms assume periodic signals on…
By using an exact analytical non-Hermitian approach in terms of resonance (quasinormal) states we express the decaying wave function as the sum of exponential and nonexponential decaying solutions to the time-dependent Schr\"odinger…
Classical phasor analysis is fundamentally limited to sinusoidal single-frequency conditions, which poses challenges when working in the presence of harmonics. Furthermore, the conventional solution, which consists of decomposing signals…
This paper reports on recent results related to audiophonic signals encoding using time-scale and time-frequency transform. More precisely, non-linear, structured approximations for tonal and transient components using local cosine and…