Search results for "Fourier serie"
showing 10 items of 38 documents
Description of intermodulation generation of nonlinear responses beyond the validity of the power series expansion
2021
Weakly nonlinear responses are commonly described by a power series expansion. However, intermodulation distortion products that cannot be described by a power series have been observed in a variety of physical systems. As the power series description is only applicable within its radius of convergence, we choose an alternative approach based on Fourier coefficients to describe intermodulation levels beyond the convergence of the power series. The description over a wide power range allows us to make a decision about models and to determine previously inaccessible model parameters. We apply the approach to data obtained from the characterization of the nonlinear dielectric susceptibility of…
Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function
2009
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Helmholtz Green function are split into their half advanced+half retarded and half advanced-half retarded components. Closed form solutions are given for these components in terms of a Horn function and a Kampe de Feriet function, respectively. The systems of partial differential equations associated with these two-dimensional hypergeometric functions are used to construct a fourth-order ordinary differential equation which both components satisfy. A s…
Localization Operators and an Uncertainty Principle for the Discrete Short Time Fourier Transform
2014
Localization operators in the discrete setting are used to obtain information on a signalffrom the knowledge on the support of its short time Fourier transform. In particular, the extremal functions of the uncertainty principle for the discrete short time Fourier transform are characterized and their connection with functions that generate a time-frequency basis is studied.
Norm-inflation results for purely BBM-type Boussinesq systems
2022
This article is concerned with the norm-inflation phenomena associated with a periodic initial-value abcd-Benjamin-Bona-Mahony type Boussinesq system. We show that the initial-value problem is ill-posed in the periodic Sobolev spaces H−sp (0, 2π)×H−sp (0, 2π) for all s > 0. Our proof is constructive, in the sense that we provide smooth initial data that generates solutions arbitrarily large in H−sp (0, 2π) × H−sp (0, 2π)-norm for arbitrarily short time. This result is sharp since in [15] the well-posedness is proved to holding for all positive periodic Sobolev indexes of the form Hsp (0, 2π) × Hsp (0, 2π), including s = 0. peerReviewed
Fourier series for elliptic integrals and some generalizations via hypergeometric series
2008
Fourier series are derived for generalizations of the three canonical Legendre incomplete elliptic integrals using a hypergeometric series approach. The Fourier series for the incomplete Epstein–Hubbell integrals are obtained as special cases of the generalization of the Legendre integrals of the first and second kinds. The Fourier series for the integrals of the first and second kinds, and those for the Epstein–Hubbell integrals, were obtained recently using a different approach, but the series obtained for the generalization of the incomplete integral of the third kind is new. All cases of the integral of the third kind are given, with the modulus and the parameter being complex variables…
PENERAPAN DERET FOURIER PADA SISTEM PENDENGARAN MANUSIA
2008
Natural vane voices comes to the humaneary on the Forier Series P(t), while the human earing system only accepts the wore of voices on the Fourier Series berhingga Q (t). The different between Fories Series P(t) and Q(l) can be eliminase using. Approximation Quadrate Smallest Method.. Therefore q(t) is a result of natural vane approach
Continuous theory of switching in geometrically confined ferroelectrics
2014
A theory of ferroelectric switching in geometrically confined samples like thin films and multilayers with domain structure has been proposed. For that we use Landau–Khalatnikov (LK) equations with free energy functional being dependent on polarization gradients. In this case, the consistent theory can be developed as for thin ferroelectric films and multilayers the domain structure reduces to Fourier series in ferroelectric polarization. The specific calculations are presented for thin film ferroelectric with dead layers and ferro-/paraelectric multilayer. Our theory is generalizable to ferroelectrics and multiferroics with other geometries.
About the reliability of the Maximum Entropy Method in reconstructing electron density: the case of MgO
2006
Abstract The reliability of the Maximum Entropy Method (MEM) to reconstruct finite temperature electron density (ED) is here discussed, investigating the case of periclase (MgO). A theoretical electron density has been generated by quantum mechanic calculations and folded with a function simulating atomic thermal motion, in order to produce a reference errorless ED [ρ(r)REF]. The Fourier coefficients of ρ(r)REF have been calculated, and used as “observed” diffraction intensities to reconstruct via MEM the original ED. The electron density attained by MEM [ρ(r)MEM] and ρ(r)REF have been compared with each other (pixel-by-pixel and critical points) to assess the ability of MEM to retrieve EDs…
2D harmonic analysis of the cogging torque in synchronous permanent magnet machines
2004
Presents an approach to determine sources of cogging torque harmonics in permanent magnet electrical machines on the basis of variations of air‐gap magnetic flux density with time and space. The magnetic flux density is determined from the two‐dimensional (2D) finite element model and decomposed into the double Fourier series through the 2D fast Fourier transform (FFT). The real trigonometric form of the Fourier series is used for the purpose to identify those space and time harmonics of magnetic flux density whose involvement in the cogging torque is the greatest relative contribution. Carries out calculations for a symmetric permanent magnet brushless machine for several rotor eccentricit…
Exponential sums related to Maass forms
2019
We estimate short exponential sums weighted by the Fourier coefficients of a Maass form. This requires working out a certain transformation formula for non-linear exponential sums, which is of independent interest. We also discuss how the results depend on the growth of the Fourier coefficients in question. As a byproduct of these considerations, we can slightly extend the range of validity of a short exponential sum estimate for holomorphic cusp forms. The short estimates allow us to reduce smoothing errors. In particular, we prove an analogue of an approximate functional equation previously proven for holomorphic cusp form coefficients. As an application of these, we remove the logarithm …