Related papers: Second-order Time-Reassigned Synchrosqueezing Tran…
Having reviewed the aspects of the linear and synchrosqueezed time-frequency representations (TFRs) needed for their understanding and correct use in Part I of this review, we now consider three more subtle issues that are nonetheless of…
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…
A class of random non-stationary signals termed timbre x dynamics is introduced and studied. These signals are obtained by non-linear transformations of sta-tionary random gaussian signals, in such a way that the transformation can be…
In this work, we propose a time-varying wave-shape extraction algorithm based on a modified version of the adaptive non-harmonic model for non-stationary signals. The model codifies the time-varying wave-shape information in the relative…
Resonance frequencies can provide useful information on the deformation occurring during fracturing experiments or $CO_2$ management, complementary to the microseismic event distribution. An accurate time-frequency representation is of…
In time reversal acoustics experiments, a signal is emitted from a localized source, recorded at an array of receivers-transducers, time reversed, and finally re-emitted into the medium. A celebrated feature of time reversal experiments is…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…
We study the problem of multi-compression and reconstructing a stochastic signal observed by several independent sensors (or compressors) that transmit compressed information to a fusion center. { The key aspect of this problem is to find…
One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often…
The decomposition of a stochastic time series into three component series representing a dual signal - namely, the mean and dispersion - while isolating noise is presented. The decomposition is performed by applying machine learning…
First-order energy dissipative schemes in time are available in literature for the Poisson-Nernst-Planck (PNP) equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite…
We introduce the construction of a orthogonal wavepacket basis set, using the concept of stroboscopic time propagation, tailored to the efficient description of non-equilibrium extended electronic systems. Thanks to three desirable…
We propose a novel formulation for phase synchronization -- the statistical problem of jointly estimating alignment angles from noisy pairwise comparisons -- as a nonconvex optimization problem that enforces consistency among the pairwise…
We present a time-domain method to detect and correct spectral alterations of signals by employing statistical characterization of waveforms and a pattern-recognition procedure using simple Artificial Neural Networks. The proposed strategy…
In time series classification and regression, signals are typically mapped into some intermediate representation used for constructing models. Since the underlying task is often insensitive to time shifts, these representations are required…
The analysis of chaotic signals with time-frequency methods is considered. For this purpose, two new transformations are presented which consist in the decomposition of a signal onto an orthogonal set of respectively linear and hyperbolic…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic,…