Related papers: Mind the step: On the frequency-domain analysis of…
Sonography techniques use multiple transducer elements for tissue visualization. Signals detected at each element are sampled prior to digital beamforming. The required sampling rates are up to 4 times the Nyquist rate of the signal and…
The potential of compressed sensing for obtaining sparse time-frequency representations for gravitational wave data analysis is illustrated by comparison with existing methods, as regards i) shedding light on the fine structure of noise…
Next-generation gravitational wave (GW) experiments will explore higher frequency ranges, where GW wavelengths approach the size of the detector itself. In this regime, GWs may be detected not just through the well-known mechanical…
In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the…
Graph signal processing extends spectral analysis to data supported on irregular domains. Existing fractional transforms for two-dimensional graph signals, including the two-dimensional graph fractional Fourier transform (GFRFT), typically…
We study the propagation, observation and control properties of the 1-d wave equation on a bounded interval discretized in space using the quadratic classical finite element approximation. A careful Fourier analysis of the discrete wave…
We derive a lower bound on the sensitivity of generic mechanical and electromagnetic gravitational wave detectors. We consider both classical and quantum detection schemes, although we focus on the former. Our results allow for a simple…
We prove a formula expressing the gradient of the phase function of a function $f: \mathbb R^d \mapsto \mathbb C$ as a normalized first frequency moment of the Wigner distribution for fixed time. The formula holds when $f$ is the Fourier…
The geodesic deviation of a pair of test particles is an natural observable for the gravitational memory effect. Nevertheless in curved spacetime, this observable is plagued with various issues that need to be clarified before one can…
In the hierarchical search for periodic sources of gravitational waves, the candidate selection, in the incoherent step, can be performed with Hough transform procedures. In this paper we analyze the problem of sensitivity loss due to…
A common technique for detection of gravitational-wave signals is searching for excess power in frequency-time maps of gravitational-wave detector data. In the event of a detection, model selection and parameter estimation will be performed…
In a number of data-driven applications such as detection of arrhythmia, interferometry or audio compression, observations are acquired indistinctly in the time or frequency domains: temporal observations allow us to study the spectral…
Gravitational waves (GWs) produce small distortions in the observable distribution of stars in the sky. We describe the characteristic pattern of astrometric deflections created by a specific gravitational waveform called a burst with…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
In this paper, we extend our method [1] for FMCW radar mutual interference mitigation (IM) based on the discrete fractional Fourier transform (DFrFT). Firstly, we propose a radar signal processing chain including our DFrFT-based IM for…
This paper determines how to define a discretely implemented Fourier transform when analysing an observed spatial point process. To develop this transform we answer four questions; first what is the natural definition of a Fourier…
We investigate the general relativistic phase of an electromagnetic wave as it propagates in the gravitational field of the Earth, which is modeled as an isolated, weakly aspherical gravitating body. We introduce coordinate systems to…
A thin two-layered waveguide is considered. The governing equations for this waveguide is a matrix Klein--Gordon equation of dimension~2. A formal solution of this system in the form of a double integral can be obtained by using Fourier…
The evolution of a quantum oscillator, with periodically varying frequency and damping, is studied in the two cases of parametric resonance (PR) producing a limited, or unlimited stretching of the wave function. The different asymptotic…
Gravitational-wave memory manifests as a permanent distortion of an idealized gravitational-wave detector and arises generically from energetic astrophysical events. For example, binary black hole mergers are expected to emit memory bursts…