Related papers: The Fourier Transform Method for Volatility Functi…
Phase retrieval from phaseless short-time Fourier transform (STFT) measurements is known to be inherently unstable when measurements are taken with respect to a single window. While an explicit inversion formula exists, it is useless in…
The nonparametric volatility estimation problem of a scalar diffusion process observed at equidistant time points is addressed. Using the spectral representation of the volatility in terms of the invariant density and an eigenpair of the…
We present a theorem concerning the invariance of cross-correlation peak positions, which provides a foundation for a new method for time difference estimation that is potentially faster than the conventional fast Fourier transform (FFT)…
In this paper, we propose two nonparametric methods used in the forecasting of functional time-dependent data, namely functional singular spectrum analysis recurrent forecasting and vector forecasting. Both algorithms utilize the results of…
Elder people consequence a variety of problems while living Activities of Daily Living (ADL) for the reason of age, sense, loneliness and cognitive changes. These cause the risk to ADL which leads to several falls. Getting real life fall…
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…
This paper presents a novel approach for estimating the modes of an observed non-stationary mixture signal. A link is first established between the short-time Fourier transform and the sparse sampling theory, where the observations are…
The frequency-domain properties of nonstationary functional time series often contain valuable information. These properties are characterized through its time-varying power spectrum. Practitioners seeking low-dimensional summary measures…
In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform (NFT). In particular, we provide…
We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…
It is shown here that precision is gained by analyzing the interferometric spectra directly from the interferograms, with no previous Fourier transformation to put them in the standard frequency domain. The method is based on the…
This paper presents a novel approach to understanding the role of harmonic dynamics and gaining a deeper appreciation for its impact within and outside of quantum mechanics. This includes consequences of harmonic dynamics and the…
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…
The time-frequency content of a signal can be measured by the Gabor transform or windowed Fourier transform. This is a function defined on phase space that is computed by taking the Fourier transform of the product of the signal against a…
In this paper phase of a signal has been viewed from a different angle. According to this view a signal can have countably infinitely many phases, one associated with each Fourier component. In other words each frequency has a phase…
We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum,…
The long therm behavior of chaotic flows is investigated by means of time dependent frequency analysis. The system under test consists of an electrically conducting fluid, confined between two differentially rotating spheres. The spherical…
Analysis of ac electrical systems can be performed via frame transformations in the time-domain or via harmonic transfer functions (HTFs) in the frequency-domain. The two approaches each have unique advantages but are hard to reconcile…
A method is described for predicting statistical properties of turbulence. Collections of Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics of the full dynamics can be…
A method is presented for investigating the periodic signal content of time series in which a number of signals is present, such as arising from the observation of multiperiodic oscillating stars in observational asteroseismology. Standard…