Related papers: Exploring Fourier methods with beer bottles
Digital filters for recursively computing the discrete Fourier transform (DFT) and estimating the frequency spectrum of sampled signals are examined, with an emphasis on magnitude-response and numerical stability. In this tutorial-style…
Traditional surface cleaning methods often suffer from drawbacks such as chemical harshness, potential for surface damage, and high energy consumption. This study investigates an alternative approach: acoustic-driven surface cleaning using…
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of…
We propose a method for recognizing moving vehicles, using data from roadside audio sensors. This problem has applications ranging widely, from traffic analysis to surveillance. We extract a frequency signature from the audio signal using a…
This is the first in a series of two papers investigating the effect of electron-phonon coupling in two-dimensional Fourier transformed electronic spectroscopy. We present a series of one- and two-dimensional nonlinear spectroscopic…
Atomic vibrations in perfect, slightly defective or mixed crystals are to a large extent well understood since many decades. Theoretical descriptions are thus in excellent agreement with the experiments. As a consequence, phonon-related…
We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions $\Sc(\mathbb R)$, and then we extend it to its dual set,…
In a duct-flute such as the recorder, steady-state oscillations are controlled by two parameters, the blowing pressure and the frequency of the acoustic resonator. As in most feedback oscillators, the oscillation amplitude is determined by…
Using molecular dynamics simulation, we study acoustic resonance in low-temperature glass by applying a small periodic shear at a boundary wall. Shear wave resonance occurs as the frequency $\omega$ approaches $\omega_\ell= \pi…
Many experiments in liquid Helium, such as the optical imaging of exploding electron bubbles, which enables research on individual particles under applied conditions, involve the usage of ultrasound generated by piezoelectric transducers.…
The first part of the paper is devoted to diffraction phenomena that can be expressed by fractional Fourier transforms whose orders are real numbers. According to a scalar theory, diffraction acts on the amplitude of the electric field as…
Resonance is an ubiquitous phenomenon present in many systems. In particular, air resonance in cavities was studied by Hermann von Helmholtz in the 1850s. Originally used as acoustic filters, Helmholtz resonators are rigid-wall cavities…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…
The model of Brownian Percolation has been introduced as an approximation of discrete last-passage percolation models close to the axis. It allowed to compute some explicit limits and prove fluctuation theorems for these, based on the…
We analyze the problem of neutrino oscillations via a fermionic particle detector model inspired by the physics of the Fermi theory of weak interactions. The model naturally leads to a description of emission and absorption of neutrinos in…
A multi-scale model is presented for predicting the magnitude and rate of powder blending in a rotating drum blender. The model combines particle diffusion coefficient correlations from the literature with advective flow field information…
The spatio-temporal dynamics of the deformation of a vibrated plate is measured by a high speed Fourier transform profilometry technique. The space-time Fourier spectrum is analyzed. It displays a behavior consistent with the premises of…
Experiments have revealed multiple quantum oscillation frequencies in underdoped high temperature superconductor $\mathrm{YBa_{2}Cu_{3}O_{6+\delta}}$, corresponding to approximately 10% doping, which contain $\mathrm{CuO}$ bilayers in the…
A highly efficient fast boundary element method (BEM) for solving large-scale engineering acoustic problems in a broad frequency range is developed and implemented. The acoustic problems are modeled by the Burton-Miller boundary integral…
We study the parametric resonance of the neutrino oscillation through the matter whose density varies spatially. The Fourier analysis of the matter effect enables us to clarify the parametric resonance condition, which is summarized in a…