Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Sinc function quadrature rules for the Fourier integral

Author: John Lund
Journal: Math. Comp. 41 (1983), 103-113
MSC: Primary 65D30
MathSciNet review: 701627
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper a numerical algorithm is proposed for the computation of the Fourier Transform. The quadrature rule developed is based on the Whittaker Cardinal Function expansion of the integrand and a certain Conformal Map. The error of the method is analyzed and numerical results are reported which confirm the accuracy of the quadrature rule.

References [Enhancements On Off] (What's this?)

  • [1] T. S. Bromwich, An Introduction to the Theory of Infinite Series, Macmillan, New York, 1966.
  • [2] G. Debalbine & J. N. Franklin, "The calculation of Fourier Integrals," Math. Comp., v. 20, 1966, pp. 570-589. MR 0203976 (34:3823)
  • [3] L. N. Filon, "On a quadrature formula for trigonometric integrals," Proc. Roy. Soc. Edinburgh, v. 49, 1929, pp. 38-47.
  • [4] M. Murwitz, Jr. & P. F. Zweifel, "Numerical quadrature of Fourier transform integrals," MTAC, v. 10, 1956, pp. 140-149. MR 0080994 (18:337h)
  • [5] V. I. Krylov & N. S. Skoblya, Handbook of Numerical Inversion of Laplace Transforms, Israel Program for Sci. Transl., Jerusalem, 1969. MR 0391481 (52:12302)
  • [6] Y. L. Luke, "On the computation of oscillatory integrals," Proc. Cambridge Philos. Soc., v. 50, 1954, pp. 269-277. MR 0062518 (15:992b)
  • [7] M. K. Miller & W. T. Guy, Jr., "Numerical inversion of the Laplace transform by use of Jacobi polynomials," SIAM J. Numer. Anal., v. 3, 1966, pp. 624-635. MR 0212995 (35:3860)
  • [8] F. W. J. Olver, Introduction to Asymptotics and Special Functions, Academic Press, New York, 1974. MR 0435697 (55:8655)
  • [9] M. E. Salzer, "Orthogonal polynomials arising in the numerical evaluations of inverse Laplace transforms," MTAC, v. 9, 1955, pp. 164-177. MR 0078498 (17:1203d)
  • [10] F. Stenger, "Integration rules via the trapezoid formula," J. Inst. Math. Appl., v. 12, 1973, pp. 103-114.
  • [11] F. Stenger, "Numerical methods based on Whittaker cardinal, or sinc functions," SIAM Rev., v. 23, 1981, pp. 165-224. MR 618638 (83g:65027)
  • [12] A. J. van de Vooren & M. J. van Linde, "Numerical calculation of integrals with strongly oscillating integrands," Math. Comp., v. 20, 1966, pp. 232-245. MR 0192644 (33:869)
  • [13] G. Walter & D. Schultz, "Some eigenfunction methods for computing a numerical Fourier transform," J. Inst. Math. Appl., v. 18, 1976, pp. 279-293. MR 0455505 (56:13743)
  • [14] M. Weber, "Numerical computation of the Fourier transform using Laguerre functions and the fast Fourier transform," Numer. Math., v. 36, 1981, pp. 197-209. MR 611492 (82c:65095)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D30

Retrieve articles in all journals with MSC: 65D30

Additional Information

Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society