The calculation of trigonometric Fourier coefficients

DOI10.1016/0021-9991(84)90138-4zbMath0559.65099OpenAlexW2027676943MaRDI QIDQ2265791

J. N. Lyness

Publication date: 1984

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9991(84)90138-4

zbMATH Keywords

fast Fourier transformequally spaced function valuestrapezoidal rule sumstrigonometric Fourier coefficients

Mathematics Subject Classification ID

Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Related Items (9)

Hyperviscous shock layers and diffusion zones: Monotonicity, spectral viscosity, and pseudospectral methods for very high order differential equations ⋮ Finite Fourier transforms computed by a modified Filon-Euler-Maclaurin method ⋮ Gibbs phenomenon and its removal for a class of orthogonal expansions ⋮ Similar basis function algorithm for numerical estimation of Fourier integrals ⋮ Accurate Reconstructions of Functions of Finite Regularity from Truncated Fourier Series Expansions ⋮ A new constructive and elementary proof of a Bernstein-Walsh theorem, improved to infinite order convergence, for functions \(C^\infty\) in an intricate but smooth two-dimensional real domain ⋮ Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of \(1/n\) ⋮ Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms ⋮ Numerical integration by means of adapted Euler summation formulas

Cites Work

• Unnamed Item
• Computational Techniques Based on the Lanczos Representation
• Adjusted Forms of the Fourier Coefficient Asymptotic Expansion and Applications in Numerical Quadrature

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