Related papers: Fourier Uniformity: An Useful Tool for Analyzing E…
Frequency is a central concept in Mathematics, Physics, and Signal Processing. It is the main tool for describing the oscillatory behavior of signals, which is usually argued to be the manifestation of some of their key features, depending…
The mechanism of synchronization of oscillations in two identical coupled flow systems has beenstudied. The time (past the coupling onset) during which a synchronous oscillation regime is establisheddepends on the oscillation phase…
Phase noise and frequency (in)stability both describe the fluctuation of stable periodic signals, from somewhat different standpoints. Frequency is unique compared to other domains of metrology, in that its fluctuations of interest span at…
The brain projects require the collection of massive electrophysiological data, aiming to the longitudinal, sectional, or populational neuroscience studies. Quality metrics automatically label the data after centralized preprocessing.…
Electroencephalograph (EEG) timeseries signals are characterized by significant noise and coarse spatial resolution, which complicates the classification of neurodegenerative diseases. Even SOTA deep learning architectures struggle to…
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…
Background: In electrical brain signals such as Local Field Potential (LFP) and Electroencephalogram (EEG), oscillations emerge as a result of neural network activity. The oscillations extend over several frequency bands. Between their…
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…
Uniform quantization is a topic that has been extensively studied. However and although an analytical description of quantization noise has been proposed, most descriptions of the spectral properties of quantization error resort to…
Quantitative helio- and asteroseismology require very precise measurements of the frequencies, amplitudes, and lifetimes of the global modes of stellar oscillation. It is common knowledge that the precision of these measurements depends on…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
Cavity-based noise detection schemes are combined with ultrafast pulse shaping as a means to diagnose the spectral correlations of both the amplitude and phase noise of an ultrafast frequency comb. The comb is divided into ten spectral…
The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…
We study the computational phase transition in a multi-frequency group synchronization problem, where pairwise relative measurements of group elements are observed across multiple frequency channels and corrupted by Gaussian noise. Using…
The use of EEG biometrics, for the purpose of automatic people recognition, has received increasing attention in the recent years. Most of current analysis rely on the extraction of features characterizing the activity of single brain…
The complex Fourier transform of the two-point correlator of the energy spectrum of a quantum system is known as the spectral form factor (SFF). It constitutes an essential diagnostic tool for phases of matter and quantum chaos. In black…
Phase synchronization was proved to be unbounded in quantum level, but the witness of phase synchronization is always expensive in terms of the quantum resource and non-local measurements involved. Based on the quantum uncertainty relation,…
An experiment to demonstrate the Fourier transform of an electric signal using the Kundt's tube is described. The results of finding the component frequencies and an approximation to the amplitudes of two sinusoidal signals which compose an…
The usual interpretation of noise is represented by a sum of many independent two-level elementary random signals with a distribution of relaxation times. In this paper it is demonstrated that also the superposition of many similar…
Electroencephalography (EEG) monitors ---by either intrusive or noninvasive electrodes--- time and frequency variations and spectral content of voltage fluctuations or waves, known as brain rhythms, which in some way uncover activity during…