Topic
Fourier series
About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.
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TL;DR: In this article, the identification of a single-input, single-output (SISO) discrete Hammerstein system is studied and the density-free pointwise convergence of the estimate is proved.
Abstract: The identification of a single-input, single-output (SISO) discrete Hammerstein system is studied. Such a system consists of a non-linear memoryless subsystem followed by a dynamic, linear subsystem. The parameters of the dynamic, linear subsystem are identified by a correlation method and the Newton-Gauss method. The main results concern the identification of the non-linear, memoryless subsystem. No conditions are imposed on the functional form of the non-linear subsystem, recovering the non-linear using the Fourier series regression estimate. The density-free pointwise convergence Of the estimate is proved, that is.algorithm converges for all input densities The rate of pointwise convergence is obtained for smooth input densities and for non-linearities of Lipschitz type.Globle convergence and its rate are also studied for a large class of non-linearities and input densities
60 citations
01 Jan 1987
TL;DR: In this paper, the stability problem of axially compressed imperfect orthotropic cylindrical shells is considered and a reliability based stochastic stability approach is described, which makes it possible to include the results of the Imperfection Sensitivity Theory directly into an Improved Shell Design Procedure.
Abstract: This paper deals with the stability problem of axially compressed imperfect orthotropic cylindrical shells. The initial imperfections are represented by a double Fourier series. Approximate solutions are derived for a single axisymmetric, a single asymmetric, a 2-modes and a multimode imperfection model. The effect of boundary conditions is studied by reducing the stability problem to the solution of a 2-point nonlinear boundary value problem. A reliability based stochastic stability approach is described, which makes it possible to include the results of the Imperfection Sensitivity Theory directly into an Improved Shell Design Procedure.
60 citations
TL;DR: The application of conformal mapping methods to the solution of free-surface flow problems is considered in this article, where they are extended to handle efficiently problems with time-dependent boundaries.
60 citations
TL;DR: Term-by-term Fourier-expansion series are used to reconstruct impurity atom distributions in muscovite mica with respect to the (001) lattice without a priori assumptions on their structures.
Abstract: Term-by-term Fourier-expansion series, each made up of components having element-specific phases and amplitudes acquired with x-ray standing wave measurements on successive orders of Bragg reflections, are used to reconstruct impurity atom distributions in muscovite mica with respect to the (001) lattice without a priori assumptions on their structures.
60 citations
TL;DR: An exact closed-form expression for the Spatial Correlation Function (SCF) is derived for 3D MIMO channels and validated results validate the proposed analytical expressions and elucidate the dependence of the system performance on azimuth and elevation angular spreads and antenna patterns.
Abstract: Previous studies have confirmed the adverse impact of fading correlation on the mutual information (MI) of two-dimensional (2D) multiple-input multiple-output (MIMO) systems. More recently, the trend is to enhance the system performance by exploiting the channels degrees of freedom in the elevation, which necessitates the derivation and characterization of three-dimensional (3D) channels in the presence of spatial correlation. In this paper, an exact closed-form expression for the Spatial Correlation Function (SCF) is derived for 3D MIMO channels. The proposed method resorts to the spherical harmonic expansion (SHE) of plane waves and the trigonometric expansion of Legendre and associated Legendre polynomials. The resulting expression depends on the underlying arbitrary angular distributions and antenna patterns through the Fourier Series (FS) coefficients of power azimuth and elevation spectrums. The novelty of the proposed method lies in the SCF being valid for any 3D propagation environment. The developed SCF determines the covariance matrices at the transmitter and the receiver that form the Kronecker channel model. In order to quantify the effects of correlation on system performance, the information-theoretic deterministic equivalents of the MI for the Kronecker model are utilized in both mono-user and multi-user cases. Numerical results validate the proposed analytical expressions and elucidate the dependence of the system performance on azimuth and elevation angular spreads and antenna patterns. Some useful insights into the behavior of MI as a function of downtilt angles are provided. The derived model will help evaluate the performance of correlated 3D MIMO channels in the future.
60 citations