Related papers: Analytic signal in many dimensions
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
We describe an analytical method for computing the orbital parameters of a planet from the periodogram of a radial velocity signal. The method is very efficient and provides a good approximation of the orbital parameters. The accuracy is…
In this paper we show that, as in the spacelike case, the inverse logarithmic expansion is applicable for all values of the argument of the analytic coupling constant. We present two different approaches, one of which is based primarily on…
The identification of sampling sets that enable unique signal recovery is fundamental to many applications in signal processing and remains a central problem in mathematical analysis. Recent studies in the mathematical literature,…
This note reviews complex and real techniques in harmonic analysis. We describe a common source of both approaches rooted in the covariant transform generated by the affine group. Keywords: wavelet, coherent state, covariant transform,…
Analytic signals constitute a class of signals that are widely applied in time-frequency analysis such as extracting instantaneous frequency (IF) or phase derivative in the characterization of ultrashort laser pulse. The purpose of this…
Conventional optical synthesis, the manipulation of the phase and amplitude of spectral components to produce an optical pulse in different temporal modes, is revolutionizing ultrafast optical science and metrology. These technologies rely…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…
Capturing high-frequency data concerning the condition of complex systems, e.g. by acoustic monitoring, has become increasingly prevalent. Such high-frequency signals typically contain time dependencies ranging over different time scales…
In this paper we study the Fourier-Laplace transform of tempered ultrahyperfunctions introduced by Sebasti\~ao e Silva and Hasumi. We establish a generalization of Paley-Wiener-Schwartz theorem for this setting. This theorem is interesting…
We prove sharp analytic regularity and decay at infinity of solutions of variable coefficients nonlinear harmonic oscillators. Namely, we show holomorphic extension to a sector in the complex domain, with a corresponding Gaussian decay,…
In this paper, we present a signal processing framework for directed graphs. Unlike undirected graphs, a graph shift operator such as the adjacency matrix associated with a directed graph usually does not admit an orthogonal eigenbasis.…
In classic graph signal processing, given a real-valued graph signal, its graph Fourier transform is typically defined as the series of inner products between the signal and each eigenvector of the graph Laplacian. Unfortunately, this…
We show that a broad class of signal acquisition schemes can be interpreted as recording data from a signal $x$ in a space $\cal U$ (typically, though not exclusively, a space of bandlimited functions) via an orthogonal projection $w =…
According to a theorem of Poincare, the solutions to differential equations are analytic functions of (and therefore have Taylor expansions in) the initial conditions and various parameters providing the right sides of the differential…
This paper considers the recovery of continuous signals in infinite dimensional spaces from the magnitude of their frequency samples. It proposes a sampling scheme which involves a combination of oversampling and modulations with complex…
Covariant phase observables are obtained by defining simple conditions for mappings from the set of phase wave functions (unit vectors of the Hardy space) to the set of phase probability densities. The existence of phase probability density…
We theoretically propose a multidimensional high-harmonic echo spectroscopy technique which utilizes strong optical fields to resolve coherent electron dynamics spanning an energy range of multiple electron Volts. Using our recently…
E-science of photometric data requires automatic procedures and a precise recognition of periodic patterns to perform science as well as possible on large data. Analytical equations that enable us to set the best constraints to properly…
Phase-space analysis or time-frequency analysis can be thought as Fourier analysis simultaneously both in time and in frequency, originating from signal processing and quantum mechanics. On groups having unitary Fourier transform, we…