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We generalize the targeted $\mathcal{B}$-statistic for continuous gravitational waves by modeling the $h_0$-prior as a half-Gaussian distribution with scale parameter $H$. This approach retains analytic tractability for two of the four…
It is a consensus in signal processing that the Gaussian kernel and its partial derivatives enable the development of robust algorithms for feature detection. Fourier analysis and convolution theory have central role in such development. In…
A typical audio signal processing pipeline includes multiple disjoint analysis stages, including calculation of a time-frequency representation followed by spectrogram-based feature analysis. We show how time-frequency analysis and…
Computing the Fourier transform of a $q$-ary function $f:\mathbb{Z}_{q}^n\rightarrow \mathbb{R}$, which maps $q$-ary sequences to real numbers, is an important problem in mathematics with wide-ranging applications in biology, signal…
We use time-frequency methods for the study of Fourier Integral operators (FIOs). In this paper we shall show that Gabor frames provide very efficient representations for a large class of FIOs. Indeed, similarly to the case of shearlets and…
Gravitational wave detectors will need optimal signal-processing algorithms to extract weak signals from the detector noise. Most algorithms designed to date are based on the unrealistic assumption that the detector noise may be modeled as…
Graph signal processing (GSP) facilitates the analysis of high-dimensional data on non-Euclidean domains by utilizing graph signals defined on graph vertices. In addition to static data, each vertex can provide continuous time-series…
This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…
Using Gabor analysis, we give a complete characterization of all lattice sampling and interpolating sequences in the Fock space of polyanalytic functions, displaying a "Nyquist rate" which increases with $n$, the degree of polyanaliticity…
We study the projection of an element of fractional Gaussian noise onto its neighbouring elements. We prove some analytic results for the coefficients of this projection, in particular, we obtain recurrence relations for them. We also make…
In financial analysis, time series modeling is often hampered by data scarcity, limiting neural network models' ability to generalize. Transfer learning mitigates this by leveraging data from similar domains, but selecting appropriate…
Interferometric gravitational-wave observatories have opened a new era in astronomy. The rich data produced by an international network enables detailed analysis of the curved space-time around black holes. With nearly one hundred signals…
As gravitational wave detectors become more advanced and sensitive, the number of signals recorded by Advanced LIGO and Virgo from merging compact objects is expected to rise dramatically. This surge in detection rates necessitates the…
Phase-space analysis or time-frequency analysis can be thought as Fourier analysis simultaneously both in time and in frequency, originating from signal processing and quantum mechanics. On groups having unitary Fourier transform, we…
A generalization of the maximum noise fraction (MNF) transform is proposed. Powers of each band are included as new bands before the MNF transform is performed. The generalized MNF (GMNF) is shown to perform better than the MNF on a time…
The local, uncorrelated multiplicative noises driving a second-order, purely noise-induced, ordering phase transition (NIPT) were assumed to be Gaussian and white in the model of [Phys. Rev. Lett. \textbf{73}, 3395 (1994)]. The potential…
Classical Graph Signal Processing (GSP) provides a robust framework for analyzing signals on irregular domains, utilizing the graph Fourier transform as a cornerstone for spectral analysis and filtering. However, as data structures grow in…
Based on a unique waveform with strong exponential localization property, an exact mathematical method for solving problems in signal analysis in time-frequency domain is presented. An analogue of the Gabor frame exposes the non-commutative…
Starting with the Wigner distribution formulation for beam wave propagation in H\"{o}lder continuous non-Gaussian random refractive index fields we show that the wave beam regime naturally leads to the white-noise scaling limit and…
In this work we review the application of the theory of Gaussian processes to the modeling of noise in pulsar-timing data analysis, and we derive various useful and optimized representations for the likelihood expressions that are needed in…