Related papers: A class of non linear adaptive time-frequency tran…
Theories unifying gravity and other interactions suggest the possibility of spatial and temporal variation of physical ``constants''. Accuracy achieved for the atomic optical frequency standards (optical clocks) approaches the level when…
In this paper, we establish a connection between the recently developed data-driven time-frequency analysis \cite{HS11,HS13-1} and the classical second order differential equations. The main idea of the data-driven time-frequency analysis…
We study the real-time dynamics retrieval from a time series via the time-frequency (TF) analysis with the minimal latency guarantee. While different from the well-known intrinsic latency definition in the filter design, a rigorous…
Time-frequency concentration operators restrict the integral analysis-synthesis formula for the short-time Fourier transform to a given compact domain. We estimate how much the corresponding eigenvalue counting function deviates from the…
We prove that for any 4 points in the plane that belong to 2 parallel lines, there is no linear dependence between the associated time-frequency translates of any nontrivial Schwartz function. If mild Diophantine properties are satisfied,…
Two-time-scale stochastic approximation, a generalized version of the popular stochastic approximation, has found broad applications in many areas including stochastic control, optimization, and machine learning. Despite its popularity,…
In this technical communique, we propose a novel observer-based adaptive scheme to deal with the parameter estimation problem of biased sinusoidal signals. Different from the existing adaptive frequency estimation scheme, the proposed…
In this paper we study the nonuniform fast Fourier transform with nonequispaced spatial and frequency data (NNFFT) and the fast sinc transform as its application. The computation of NNFFT is mainly based on the nonuniform fast Fourier…
Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…
For multivariate stationary time series many important properties, such as partial correlation, graphical models and autoregressive representations are encoded in the inverse of its spectral density matrix. This is not true for…
We present new tight bounds for averaging differential inclusions, which we apply to multi-frequency inclusions consisting of a sum of time periodic set-valued mappings. For this family of inclusions we establish an a tight estimate of…
The synchrosqueezing transform, a kind of reassignment method, aims to sharpen the time-frequency representation and to separate the components of a multicomponent non-stationary signal. In this paper, we consider the short-time Fourier…
The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency…
For a broad class of nonlinear time series known as Bernoulli shifts, we establish the asymptotic normality of the smoothed periodogram estimator of the long-run variance. This estimator uses only a narrow band of Fourier frequencies around…
Clock synchronisation relies on time-frequency transfer procedures which involve quantum fields. We use the conformal symmetry of such fields to define as quantum operators the time and frequency exchanged in transfer procedures and to…
Time series anomaly detection is critical for system monitoring and risk identification, across various domains, such as finance and healthcare. However, for most reconstruction-based approaches, detecting anomalies remains a challenge due…
In this paper the analogues of the Lorentz transformations for non-inertial reference frames have been obtained. A common case when the movement speed of one coordinate frame in relation to another one can have time derivatives of higher…
Time series classification (TSC) is fundamental in numerous domains, including finance, healthcare, and environmental monitoring. However, traditional TSC methods often struggle with the inherent complexity and variability of time series…
Many chemical processes exhibit diverse timescale dynamics with a strong coupling between timescale sensitive variables. Model predictive control with a non-uniformly spaced optimisation horizon is an effective approach to multi-timescale…
The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the…