Related papers: The Gaussian Wave Packet Transform via Quadrature …
We present the Fourier Transform of a continuous gravitational wave. We have analysed the data set for one day observation time and our analysis is applicable for arbitrary location of detector and source. We have taken into account the…
Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint…
The effective quantum field theory description of gravity, despite its non-renormalizability, allows for predictions beyond classical general relativity. As we enter the age of gravitational wave astronomy, an important and timely question…
We connect three phenomena of wave packet dynamics: Talbot images, revivals of a particle in a box and fractional revivals. The physical origin of these effects is deeply rooted in phase factors which are quadratic in the quantum number. We…
In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…
Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to…
Wavelet transforms are widely used in various fields of science and engineering as a mathematical tool with features that reveal information ignored by the Fourier transform. Unlike the Fourier transform, which is unique, a wavelet…
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…
Resonant transmission occurs when constructive interference results in the complete passage of an incoming wave through an array of barriers. In this paper we explore such a scenario with one dimensional models. We adopt wave packets with…
The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half. Quantum revivals are characterized by initially…
Fourier expansion of the integrand in the path integral formula for the partition function of quantum systems leads to a deterministic expression which, though still quite complex, is easier to process than the original functional integral.…
With the development of data acquisition technology, large amounts of multi-channel data are collected and widely used in many fields. Most of them, such as RGB images and vector fields, can be expressed as different types of multi-channel…
Stieltjes, Perron, and Markov in analysis of the moment problem, for absolutely continuous measures, constructed the underlying measure as the discontinuity across the cut of a Cauchy representation of an otherwise real-analytic function.…
In this paper we obtain the Fourier Transform of a continuous gravitational wave. We have analysed the data set for (i) one year observation time and (ii) arbitrary observation time, for arbitrary location of detector and source taking into…
We analyze the semiclassical evolution of Gaussian wavepackets in chaotic systems. We prove that after some short time a Gaussian wavepacket becomes a primitive WKB state. From then on, the state can be propagated using the standard TDWKB…
The Hilbert transform (HT) and associated Gabor analytic signal (GAS) representation are well-known and widely used mathematical formulations for modeling and analysis of signals in various applications. In this study, like the HT, to…
The algorithm of modified wavelet analysis is discussed. It is based on the weighted least squares approximation. Contrary to the Gaussian as a weight function, we propose to use a compact weight function. The accuracy estimates using the…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
A consistent constructive covariant description of neutrino flavour transition amplitude in vacuum is presented. To this end a special generalized relativistic wave packet is constructed with correct extension onto the higher spins. This…
Normalized wave packets express particles in nature. Their sizes are determined by their interactions with matter, and depend on environments. Nevertheless, these characterize scatterings processes in realistic situations, and govern the…