Related papers: Time-frequency analysis of bivariate signals
A novel single-frame quaternion estimator processing two vector observations is introduced. The singular cases are examined, and appropriate rotational solutions are provided. Additionally, an alternative method involving sequential…
We examine three experimental observations of Faraday waves generated by two-frequency forcing, in which a primary hexagonal pattern becomes unstable to three different superlattice patterns. We use the symmetry-based approach developed by…
Multivariate time series forecasting is a pivotal task in several domains, including financial planning, medical diagnostics, and climate science. This paper presents the Neural Fourier Transform (NFT) algorithm, which combines…
Fourier transform-based methods enable accurate, dispersion-free simulations of time-domain scattering problems by evaluating solutions to the Helmholtz equation at a discrete set of frequencies sufficient to approximate the inverse Fourier…
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…
In this paper we address the problem of constructing a feature extractor which combines Mallat's scattering transform framework with time-frequency (Gabor) representations. To do this, we introduce a class of frames, called uniform covering…
We use dispersive Fourier transformation to measure shot-to-shot spectral instabilities in femtosecond supercontinuum generation. We study both the onset phase of supercontinuum generation with distinct dispersive wave generation, as well…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has…
Spectrotemporal encoding of optical quantum information is emerging as a powerful tool in quantum information technology. Processing of spectrotemporal information has recently been demonstrated in multi-mode quantum memories, based on…
Modeling turbulent flows by a random Fourier decomposition is a classical procedure in order to use simplified models of turbulence in heat transport and other applications. We carefully investigate the Fourier time series of…
Spectra of ordered eigenvalues of finite Random Matrices are interpreted as a time series. Dataadaptive techniques from signal analysis are applied to decompose the spectrum in clearly differentiated trend and fluctuation modes, avoiding…
Time-varying graph signals are alternative representation of multivariate (or multichannel) signals in which a single time-series is associated with each of the nodes or vertex of a graph. Aided by the graph-theoretic tools, time-varying…
We present measurements of the complete spatio-temporal Fourier spectrum of Faraday waves. The Faraday waves are generated at the interface of two immiscible index matched liquids of different density. By use of a new absorption technique…
This algorithm is designed to perform numerical transforms to convert data from the temporal domain into the spectral domain. This algorithm obtains the spectral magnitude and phase by studying the Coefficient of Determination of a series…
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…
A Fourier transform method is introduced for a class of hybrid time-frequency methods that solve the acoustic scattering problem in regimes where the solution exhibits both highly oscillatory behavior and slow decay in time. This extends…
There is a class of physical filtration processes where the input is adequately modeled by a continuous periodic function f (x) of bounded variation over its period, and the output depends only on certain harmonics of the Fourier expansion…
We introduce a scattering representation for the analysis and classification of sounds. It is locally translation-invariant, stable to deformations in time and frequency, and has the ability to capture harmonic structures. The scattering…
Radio interferometers consisting of identical antennas arranged on a regular lattice permit fast Fourier transform beamforming, which reduces the correlation cost from $\mathcal{O}(n^2)$ in the number of antennas to $\mathcal{O}(n\log n)$.…