Related papers: Mind the step: On the frequency-domain analysis of…
This report will explore and answer fundamental questions about taking Fourier Transforms and tying it with recent advances in AI and neural architecture. One interpretation of the Fourier Transform is decomposing a signal into its…
We demonstrate both theoretically and experimentally that the harmonics from abruptly auto-focusing ring-Airy beams present a surprising property, they preserve the phase distribution of the fundamental beam. Consequently, this "phase…
Recent interest in the "memory effect" prompted us to revisit the relation of gravitational aves and oscillators. 50 years ago Niederer [1] found that an isotropic harmonic oscillator with a constant frequency can be mapped onto a free…
This study introduces the Bragg Frequency Convertor, a spatial-temporal-periodic grating that extends the concept of conventional Bragg gratings into the dynamic domain to achieve pure parametric frequency conversion. By time-modulating…
Fast Fourier Transform (FFT) relies on the HRV frequency-domain analysis techniques. It requires re-sampling of the inherently unevenly sampled heartbeat time-series (RR tachogram) to produce an evenly sampled time series of the heartbeat.…
We propose a quantum memory protocol based on dynamically changing the resonance frequency of an ensemble of two-level atoms. By sweeping the atomic frequency in an adiabatic fashion, photons are reversibly transferred into atomic…
We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…
Gravitational-wave displacement memory is a remarkable and ubiquitous phenomenon predicted by general relativity, which has not yet been detected. Unlike the oscillatory components of gravitational waveforms, displacement memory is…
We propose a novel approach to detecting the elusive gravitational-wave memory predicted by general relativity to accompany black hole mergers: direct measurement of the permanent space-time strain offset. Compared to previous techniques…
Decomposing multivariate time series with certain basic dynamics is crucial for understanding, predicting and controlling nonlinear spatiotemporally dynamic systems such as the brain. Dynamic mode decomposition (DMD) is a method for…
We propose a quantum memory protocol based on trapping photons in a fiber-integrated cavity, comprised of a birefringent fiber with dichroic reflective end facets. Photons are switched into resonance with the fiber cavity by intracavity…
The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science. Fourier phase retrieval poses fundamental theoretical and…
This paper introduces a novel technique to preserve spectral features in lossy compression based on a novel fast Fourier correction algorithm\added{ for regular-grid data}. Preserving both spatial and frequency representations of data is…
This paper proposes a novel, rigorous and simple Fourier-transformation approach to study resonances in a perfectly conducting slab with finite number of subwavelength slits of width $h\ll 1$. Since regions outside the slits are variable…
In geophysical environments, wave motions that are shaped by the action of gravity and global rotation bear the name of gravito-inertial waves. We present a geometrical description of gravito-inertial surface waves, which are low-frequency…
The study points out that the traditional solutions to wave equation of dissipative wave and motion equation of block for a multi-degree-of-freedom mass spring damper system are the possible solutions, which are not necessarily objective…
It is expected that the quantum nature of spacetime leaves its imprint in all semiclassical gravitational systems, at least in certain regimes, including gravitational waves. In this paper we investigate such imprints on gravitational waves…
Injectivity of the continuous wavelet transform acting on a square integrable signal is proved under weak conditions on the Fourier transform of the wavelet, namely that it is nonzero somewhere in almost every direction. For a bounded…
We show how frequency fluctuations of a vibrational mode can be separated from other sources of phase noise. The method is based on the analysis of the time dependence of the complex amplitude of forced vibrations. The moments of the…
In the digital world, signals are discrete and finite. The Fourier representation of discrete and finite signals is FT convolution of the finite sampling function and the continuous signal. Conventionally, finite sampling is treated as a…