Topic

# Fourier series

About: Fourier series is a(n) research topic. Over the lifetime, 16548 publication(s) have been published within this topic receiving 322486 citation(s).

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TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.

Abstract: An efficient method for the calculation of the interactions of a 2' factorial ex- periment was introduced by Yates and is widely known by his name. The generaliza- tion to 3' was given by Box et al. (1). Good (2) generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series. In their full generality, Good's methods are applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices, where m is proportional to log N. This results inma procedure requiring a number of operations proportional to N log N rather than N2. These methods are applied here to the calculation of complex Fourier series. They are useful in situations where the number of data points is, or can be chosen to be, a highly composite number. The algorithm is here derived and presented in a rather different form. Attention is given to the choice of N. It is also shown how special advantage can be obtained in the use of a binary computer with N = 2' and how the entire calculation can be performed within the array of N data storage locations used for the given Fourier coefficients. Consider the problem of calculating the complex Fourier series N-1 (1) X(j) = EA(k)-Wjk, j = 0 1, * ,N- 1, k=0

10,975 citations

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TL;DR: In this paper, a simulation program for particle-mesh force calculation is presented, based on a one-dimensional plasma model and a collisionless particle model, which is used to simulate collisionless particle models.

Abstract: Computer experiments using particle models A one-dimensional plasma model The simulation program Time integration schemes The particle-mesh force calculation The solution of field equations Collisionless particle models Particle-particle/particle-mesh algorithms Plasma simulation Semiconductor device simulation Astrophysics Solids, liquids and phase changes Fourier transforms Fourier series and finite Fourier transforms Bibliography Index

6,236 citations

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01 Jun 1961

TL;DR: In this paper, a revised version of the Revised edition of the book has been published, with a new introduction to the concept of plane wave functions and spherical wave functions, as well as a detailed discussion of the properties of these functions.

Abstract: Foreword to the Revised Edition. Preface. Fundamental Concepts. Introduction to Waves. Some Theorems and Concepts. Plane Wave Functions. Cylindrical Wave Functions. Spherical Wave Functions. Perturbational and Variational Techniques. Microwave Networks. Appendix A: Vector Analysis. Appendix B: Complex Permittivities. Appendix C: Fourier Series and Integrals. Appendix D: Bessel Functions. Appendix E: Legendre Functions. Bibliography. Index.

5,482 citations

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01 Jan 1977

TL;DR: Spectral Methods Survey of Approximation Theory Review of Convergence Theory Algebraic Stability Spectral Methods Using Fourier Series Applications of algebraic stability analysis Constant Coefficient Hyperbolic Equations Time Differencing Efficient Implementation of Spectral Method as discussed by the authors.

Abstract: Spectral Methods Survey of Approximation Theory Review of Convergence Theory Algebraic Stability Spectral Methods Using Fourier Series Applications of Algebraic Stability Analysis Constant Coefficient Hyperbolic Equations Time Differencing Efficient Implementation of Spectral Methods Numerical Results for Hyperbolic Problems Advection-Diffusion Equation Models of Incompressible Fluid Dynamics Miscellaneous Applications of Spectral Methods Survey of Spectral Methods and Applications Properties of Chebyshev and Legendre Polynomial Expansions.

3,243 citations

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TL;DR: A program for calculating the semi-classic transport coefficients is described, based on a smoothed Fourier interpolation of the bands, which in principle should be exact within Boltzmann theory.

Abstract: A program for calculating the semi-classic transport coefficients is described. It is based on a smoothed Fourier interpolation of the bands. From this analytical representation we calculate the derivatives necessary for the transport distributions. The method is compared to earlier calculations, which in principle should be exact within Boltzmann theory, and a very convincing agreement is found.

2,936 citations