Calculating Fourier Transforms of Long-Tailed Functions
Copyright policy )Calculating Fourier Transforms of Long-Tailed Functions
We describe a method for evaluating Fourier transform functions numerically when function values f(x) are available for any value of x. Our method is based on the Möbius inversion of the Poisson summation formula, and employs a nonlinear series acceleration technique. Numerical evidence suggests that, for relatively smooth functions having long tails, this approach may be very useful.
- Argonne National Laboratory United States
Extrapolation to the limit, deferred corrections, long-tailed functions, Numerical methods for trigonometric approximation and interpolation, Poisson summation formula, fast Fourier transform, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Fourier transform functions, trapezoidal quadrature rule, nonlinear series acceleration, Acceleration of convergence in numerical analysis, Möbius inversion
Extrapolation to the limit, deferred corrections, long-tailed functions, Numerical methods for trigonometric approximation and interpolation, Poisson summation formula, fast Fourier transform, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Fourier transform functions, trapezoidal quadrature rule, nonlinear series acceleration, Acceleration of convergence in numerical analysis, Möbius inversion
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