Related papers: Fourier Uniformity: An Useful Tool for Analyzing E…
We radically simplify coherently averaged dual-comb spectroscopy by introducing a real-time self-correction system: a radio frequency system-on-chip computes each incoming dual-comb interferogram's phase, frequency, and arrival time;…
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…
We demonstrate that extremely rapid and weak periodic and non-periodic signals can easily be detected by using the autocorrelation of intensity as a function of time. We use standard radio-astronomical observations that have artificial…
Much work over the last 25 years has demonstrated that the interface-specific, alloptical technique, vibrational sum frequency generation (v-SFG) spectroscopy, is often uniquely capable of characterizing the structure and dynamics of…
The electroencephalography (EEG) source imaging problem is very sensitive to the electrical modelling of the skull of the patient under examination. Unfortunately, the currently available EEG devices and their embedded software do not take…
The stability of the phase difference between two white-light continua, generated from the same 180-fs pulses at 1035\,nm, is assessed by a modified Bellini-Hansch interferometer. Mutual spectral stability is studied as a function of…
We consider the electrical signals recorded from a subdural array of electrodes placed on the pial surface of the brain for chronic evaluation of epileptic patients before surgical resection. A simple and computationally fast method to…
The variation of the velocity of a periodic signal and its frequency along the world line of a standard emitter (at rest with an observer) are considered in a space with affine connections and metrics. It is shown that the frequency of the…
Neural synchronization is believed to be critical for many brain functions. It frequently exhibits temporal variability, but it is not known if this variability has a specific temporal patterning. This study explores these…
We describe a Fourier transform spectroscopy technique for directly measuring band structures, and apply it to a spin-1 spin-orbit coupled Bose-Einstein condensate. In our technique, we suddenly change the Hamiltonian of the system by…
We use Fourier analysis to access risk in financial products. With it we analyze price changes of e.g. stocks. Via Fourier analysis we scrutinize quantitatively whether the frequency of change is higher than a change in (conserved) company…
When sampling multiple signals, the correlation between the signals can be exploited to reduce the overall number of samples. In this paper, we study the sampling theory of multiple correlated signals, using correlation to sample them at…
Data uniformity is a concept associated with several semantic data characteristics such as lack of features, correlation and sample bias. This article introduces a novel measure to assess data uniformity and detect uniform pointsets on…
It is well-known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as…
Phase synchronization refers to a kind of collective phenomenon that the phase difference between two or more systems is locked, and it has widely been investigated between systems with the identical physical properties, such as the…
EEG time series are analyzed using the diffusion entropy method. The resulting EEG entropy manifests short-time scaling, asymptotic saturation and an attenuated alpha-rhythm modulation. These properties are faithfully modeled by a…
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…
An inversion of the speech polarity may have a dramatic detrimental effect on the performance of various techniques of speech processing. An automatic method for determining the speech polarity (which is dependent upon the recording setup)…
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple…
In this paper, we study the phase transition behavior emerging from the interactions among multiple agents in the presence of noise. We propose a simple discrete-time model in which a group of non-mobile agents form either a fixed connected…