Related papers: Instantaneous frequency and wave shape functions (…
It is widely held that identical systems tend to behave similarly under comparable conditions. Yet, for systems that interact through a network, symmetry breaking can lead to scenarios in which this expectation does not hold. Prominent…
The notion of a physical collapse of the wave function is embodied in dynamical collapse models. These involve a modification of the unitary evolution of the wave function such as to give a dynamical account of collapse. The resulting…
This article consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. Also an efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet.…
Turbulence is known to show intermittency. That is, statistical properties vary with the length scale in a way not accounted for by statistical similarity where dimensionless ratios of moments are constant. Intermittency occurs even in the…
Periodic point sets model all solid crystalline materials whose structures are determined in a rigid form and should be studied up to rigid motion or isometry preserving inter-point distances. In 2021 H.Edelsbrunner et al. introduced an…
Gravitational wave astronomy relies on the use of multiple detectors, so that coincident detections may distinguish real signals from instrumental artifacts, and also so that relative timing of signals can provide the sky position of…
We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has mass and charge density distributing in space,…
Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random…
We derive the exact expression for the resonant frequency of the time-averaged steady-state energy and show that this frequency is excellently approximated by the arithmetic mean of the amplitude and velocity resonant frequencies. In…
Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
High-resolution time-frequency (TF) analysis plays crucial role in characterizing multicomponent signal (MCSs) and estimating oscillatory properties. Linear time-frequency representations (TFRs) such as classical short-time Fourier…
We explain why aliasing can be detected in a generic temporally-sampled stationary signal process. We then define a concept of stationarity that makes sense for single waveforms. (This is done without assuming that the waveform is a sample…
An arbitrary optical waveform can be synthesized by complex-frequency waves as well as by realfrequency harmonic waves. While single complex-frequency wave with exponentially rising waveform can be perfectly absorbed in lossless structures.…
This paper introduces a general and flexible framework for F0 and aperiodicity (additive non periodic component) analysis, specifically intended for high-quality speech synthesis and modification applications. The proposed framework…
Recently the study of modeling a non-stationary signal as a superposition of amplitude and frequency-modulated Fourier-like oscillatory modes has been a very active research area. The synchrosqueezing transform (SST) is a powerful method…
Bicoherence analysis is a well established method for identifying the quadratic nonlinearity of stationary processes. However, it is often applied without checking the basic assumptions of stationarity and convergence. The classic…
We achieve the multifractal analysis of a class of complex valued statistically self-similar continuous functions. For we use multifractal formalisms associated with pointwise oscillation exponents of all orders. Our study exhibits new…
Time-frequency representations are important for the analysis of time series. We have developed an online time-series analysis system and equipped it to reliably handle re-alignment in the time-frequency plane. The system can deal with…
We study the random sampling of the short-time Fourier transform of functions that are localized in a compact region in the time-frequency plane. We follow the approach introduced by Bass and Gr\"ochenig for band-limited functions, and show…
Waves propagating through weakly disordered smooth linear media undergo a universal phenomenon called branched flow. Branched flow has been observed and studied experimentally in various systems by considering coherent waves. Recent…