Related papers: One More Tool for Understanding Resonance
Quantum group Fourier transform methods are applied to the study of processes on noncommutative Minkowski spacetime $[x^i,t]=\imath\lambda x^i$. A natural wave equation is derived and the associated phenomena of {\it in vacuo} dispersion…
Radiation by elementary sources is a basic problem in wave physics. We show that the time-domain energy flux radiated from electromagnetic and acoustic subwalength sources exhibits remarkable features. In particular, a subtle trade-off…
Resonances leave prominent signatures in atomic and molecular ionization triggered by the absorption of single or multiple photons. These signatures reveal various aspects of the ionization process, characterizing both the initial and final…
The rapid and accurate evaluation of convolutions with singular kernels plays crucial roles in a wide range of scientific and engineering applications. Building on the recently introduced Truncated Fourier Filtering method for smooth…
Modeling turbulent flows by a random Fourier decomposition is a classical procedure in order to use simplified models of turbulence in heat transport and other applications. We carefully investigate the Fourier time series of…
Imaging by aperture synthesis from interferometric data is a well-known, but is a strong ill-posed inverse problem. Strong and faint radio sources can be imaged unambiguously using time and frequency integration to gather more Fourier…
Ring-array ultrasound computed tomography has recently achieved sufficient maturity for clinical applications like breast imaging. Image reconstruction is achieved with state of art iterative algorithms (full waveform inversion in the…
Interferometric detectors will very soon give us an unprecedented view of the gravitational-wave sky, and in particular of the explosive and transient Universe. Now is the time to challenge our theoretical understanding of short-duration…
The problem of denoising a one-dimensional signal possessing varying degrees of smoothness is ubiquitous in time-domain astronomy and astronomical spectroscopy. For example, in the time domain, an astronomical object may exhibit a smoothly…
The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…
This paper explores the innovative application of the Fractional Fourier Transform (FrFT) in sound synthesis, highlighting its potential to redefine time-frequency analysis in audio processing. As an extension of the classical Fourier…
Recent gravitational wave observations show evidence for the presence of higher harmonics, thus possibly indicating that these waves were generated in the inspiral of compact objects with asymmetric mass ratios. Signals with higher…
In this paper we introduce the temporally factorized 3D convolution (3TConv) as an interpretable alternative to the regular 3D convolution (3DConv). In a 3TConv the 3D convolutional filter is obtained by learning a 2D filter and a set of…
The advent of novel nonlinear materials has stirred unprecedented interest in exploring the use of temporal inhomogeneities to achieve novel forms of wave control, amidst the greater vision of engineering metamaterials across both space and…
We present a method of mode analysis to search for signals with frequency evolution and limited duration in a given data stream. Our method is a natural expansion of the Fourier analysis, and we can obtain the information about frequency…
Image inpainting plays a vital role in restoring missing image regions and supporting high-level vision tasks, but traditional methods struggle with complex textures and large occlusions. Although Transformer-based approaches have…
For the first time, complete source distributions for the emission and absorption of acoustic and electromagnetic wavelets are defined and computed, both in spacetime and Fourier space. The biggest surprise is the great simplicity of the…
Transform image processing methods are methods that work in domains of image transforms, such as Discrete Fourier, Discrete Cosine, Wavelet and alike. They are the basic tool in image compression, in image restoration, in image re-sampling…
Patterns in temporal data can often be found across different scales, such as days, weeks, and months, making effective visualization of time-based data challenging. Here we propose a new approach for providing focus and context in…
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…