NDLI: Algorithm 418: calculation of Fourier integrals [D1]

Content Provider	ACM Digital Library
Author	Einarsson, Bo
Abstract	The most commonly used formula for calculating Fourier integrals is Filon's formula, which is based on the approximation of the function by a quadratic in each double interval. In order to obtain a better approximation the cubic spline fit is used in [1]. The obtained formulas do not need the explicit calculation of the spline fit, but in addition to the function values at all intermediate points, the values of the first and second derivatives at the boundary points are required. However, these values are often obtained from symmetry conditions. If the derivatives at the end-points are unknown, they may be calculated from a cubic spline fit, for example by using some exterior points or by using two extra interior conditions for the spline fit. It can also be noted that in certain periodic cases the terms containing the derivatives will cancel, and their values will be superfluous. The use of Algorithm 353 [2] is recommended if the frequency ω/π is a positive integer and the interval is [0,1]. Test computations reported in [1] indicate that the spline formula is more accurate than Filon's formula. Both are of the fourth order. The expansion of the error term in powers of the step length contains only even powers, and therefore the use of Richardson extrapolation is very efficient.
Starting Page	47
Ending Page	49
Page Count	3
File Format	PDF
ISSN	00010782 15577317
DOI	10.1145/361237.361250
Journal	Communications of the ACM (CACM)
Volume Number	15
Issue Number	1
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2005-08-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Quadrature Fourier integrals Extrapolation Integration Filon integration Filon quadrature Spline quadrature Richardson extrapolation Fourier series Fourier coefficients Spline Spline approximation
Content Type	Text
Resource Type	Article
Subject	Computer Science Computer Science

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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Remark on algorithm 418 [D1]

Algorithm 353: Filon quadrature [D1]

Remark on algorithm 353 [D1]: Filon quadrature

Algorithm 427: Fourier cosine integral [D1]

An algorithm for Filon quadrature

Remark on algorithm 418: calculation of Fourier integrals

Algorithm 468: algorithm for automatic numerical integration over a finite interval [D1]

Remark on algorithm 331: Gaussian quadrature formulas [D1]

Certification of algorithm 379 [D1]

Algorithm 418: calculation of Fourier integrals [D1]

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