Related papers: Mind the step: On the frequency-domain analysis of…
We study the gravitational wave memory effect in spacetimes related to flat space by a conformal transformation. The discussion is general but the gravitational wave length scale is assumed to be small compared with the background curvature…
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…
The ringdown part of gravitational waves in the final stage of merger of compact objects tells us the nature of strong gravity which can be used for testing the theories of gravity. The ringdown waveform, however, fades out in a very short…
The complex wave representation (CWR) converts unsigned 2D distance transforms into their corresponding wave functions. Here, the distance transform S(X) appears as the phase of the wave function \phi(X)---specifically,…
In this paper we describe a model for the $(\ell=2, m=0)$ spherical harmonic mode of the gravitational wave signal emitted by the coalescence of binary black holes, in particular, spin-aligned systems. This mode can be viewed as consisting…
The energy radiated (without the 1.5PN tail contribution which requires a different treatment) by a binary system of compact objects moving in a hyperboliclike orbit is computed in the frequency domain through the second post-Newtonian…
In phase unwrapping, the locations and densities of residues are indicative of the severity of the unwrapping problem. The residues are used to detect and evade inconsistent phase areas. Gdeisat et al. proposed an algorithm to increase the…
Accurately modeling the inspiral-merger-ringdown (IMR) signal of coalescing compact objects is essential for the test of general relativity. However, it is known that astrophysical environments can distort gravitational-wave (GW) signal…
This technical note is on digital filters for the high-fidelity estimation of a sinusoidal signal's frequency in the presence of additive noise. The complex noise is assumed to be white (i.e. uncorrelated) however it need not be Gaussian.…
This article aims at comparing gravitational wave memory effect in a Schwarzschild spacetime with that of other compact objects with static and spherically symmetric spacetime, with the purpose of proposing a procedure for differentiating…
In many particle physics models, domain wall can form during the phase transition process after discrete symmetry breaking. We study the scenario within a complex singlet extended Standard Model framework, where a strongly first order phase…
The spectrum of the quasinormal modes of the gravitational waves emitted during the ringdown phase following the merger of two black holes is of primary importance in gravitational astronomy. However, the spectrum is extremely sensitive to…
A central challenge in probing the quantum nature of gravity is to distinguish effects that are genuinely quantum from those that can be explained classically. In this work, we study how quantized gravitational waves interact with thermal…
Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of…
Spectral analysis provides one of the most effective paradigms for information-preserving dimensionality reduction, as simple descriptions of naturally occurring signals are often obtained via few terms of periodic basis functions. In this…
Electromagnetic methods recently proposed for detecting gravitational waves modify the Michelson phase shift analysis (historically employed for special relativity). We suggest that a frequency modulation analysis is more suited to general…
In the first paper in this series, a class of observables that generalized the gravitational wave memory effect were introduced and given the name "persistent gravitational wave observables." These observables are all nonlocal in time,…
There is a class of physical filtration processes where the input is adequately modeled by a continuous periodic function f (x) of bounded variation over its period, and the output depends only on certain harmonics of the Fourier expansion…
This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to…
A spatial signal is defined by its evaluations on the whole domain. In this paper, we consider stable reconstruction of real-valued signals with finite rate of innovations (FRI), up to a sign, from their magnitude measurements on the whole…