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The short-time Fourier transform (STFT) is widely used for analyzing non-stationary signals. However, its performance is highly sensitive to its parameters, and manual or heuristic tuning often yields suboptimal results. To overcome this…
We propose the Fourier-domain transfer entropy spectrum, a novel generalization of transfer entropy, as a model-free metric of causality. For arbitrary systems, this approach systematically quantifies the causality among their different…
Although instantaneous interactions are unphysical, a large variety of maximum entropy statistical inference methods match the model-inferred and the empirically-measured equal-time correlation functions. Focusing on collective motion of…
The nonlinear Fourier transform has the potential to overcome limits on performance and achievable data rates which arise in modern optical fiber communication systems when nonlinear interference is treated as noise. The periodic nonlinear…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
Recently, it has been shown that incoherence is an unrealistic assumption for compressed sensing when applied to many inverse problems. Instead, the key property that permits efficient recovery in such problems is so-called local…
The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can…
Despite being the most popular methods of data analysis, Fourier-based techniques suffer from the problem of static resolution that is currently believed to be a fundamental limitation of the Fourier Transform. Although alternative…
Chaotic synchronization is generally extremely sensitive to the presence of noise and other inference in the channel. Is this sensitivity a fundamental property of chaotic synchronization or is it related to the choice of synchronization…
The "theoretical limit of time-frequency resolution in Fourier analysis" is thought to originate in certain mathematical and/or physical limitations. This, however, is not true. The actual origin arises from the numerical (technical) method…
This paper is devoted to the estimation of the shift parameter in a semiparametric regression model when the distribution of the observation times is unknown. Hence, we propose to use a stochastic algorithm which takes into account the…
Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…
We describe a method to probe the spectral fluctuations of a transition over broad ranges of frequencies and timescales with the high spectral resolution of Fourier spectroscopy, and a temporal resolution as high as the excited state…
In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalised shrinkage technique…
In this paper we show how to use Fourier transform methods to analyze the asymptotic behavior of kernel distribution function estimators. Exact expressions for the mean integrated squared error in terms of the characteristic function of the…
We consider sensor array imaging for simultaneous noise blended sources. We study a migration imaging functional and we analyze its sensitivity to singular perturbations of the speed of propagation of the medium. We consider two kinds of…
Model-free adaptive optimization methods are capable of optimizing unknown, time-varying processes even when other optimization methods are not. However, their practical application is often limited by perturbations that are used to gather…
Although one can formulate an intuitive notion of instantaneous frequency, generalizing "frequency" as we understand it in e.g. the Fourier transform, a rigorous mathematical definition is lacking. In this paper, we consider a class of…
The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed It\^o processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic…
Phase difference function is established by means of phase transfer function between time domains of source and interference point. The function reveals a necessary interrelation between outcome of two-beam interference, source's frequency…