## Evaluation of Fourier integrals using $B$-splines

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- by M. Lax and G. P. Agrawal PDF
- Math. Comp.
**39**(1982), 535-548 Request permission

Corrigendum: Math. Comp.

**43**(1984), 347.

Corrigendum: Math. Comp.

**43**(1984), 347.

## Abstract:

Finite Fourier integrals of functions possessing jumps in value, in the first or in the second derivative, are shown to be evaluated more efficiently, and more accurately, using a continuous Fourier transform (CFT) method than the discrete transform method used by the fast Fourier transform (FFT) algorithm. A*B*-spline fit is made to the input function, and the Fourier transform of the set of

*B*-splines is performed analytically for a possibly nonuniform mesh. Several applications of the CFT method are made to compare its performance with the FFT method. The use of a 256-point FFT yields errors of order ${10^{ - 2}}$, whereas the same information used by the CFT algorithm yields errors of order ${10^{ - 7}}$—the machine accuracy available in single precision. Comparable accuracy is obtainable from the FFT over the limited original domain if more than 20,000 points are used.

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## Additional Information

- © Copyright 1982 American Mathematical Society
- Journal: Math. Comp.
**39**(1982), 535-548 - MSC: Primary 65D30; Secondary 42A15, 65R10
- DOI: https://doi.org/10.1090/S0025-5718-1982-0669645-5
- MathSciNet review: 669645