The fast Fourier transform algorithm: Programming considerations in the calculation of sine, cosine and Laplace transforms

doi:10.1016/0022-460X(70)90075-1

Journal of Sound and Vibration

Volume 12, Issue 3, July 1970, Pages 315-337

https://doi.org/10.1016/0022-460X(70)90075-1 Get rights and content

Abstract

In the organization of programming packages for computing Fourier and Laplace transforms, it is useful, both for conceptual understanding and for operational efficiency to consider the discrete complex Fourier transform as a kind of nucleus around which programming for special applications is performed. An advantage of these procedures is that the basic complex Fourier transform algorithm is systematic and can relatively easily be implemented in efficient subroutines, micro-programs and special hardware devices. Once this is done, programming for special properties of the data can efficiently be left to the user to implement on a general purpose computer.

The problem of establishing the correspondence between the discrete transforms and the continuous functions with which one is usually dealing is described. The application of these results and the above-mentioned subroutines to the calculation and inversion of Laplace transforms is given with formulas and empirical results displaying the effect of optimal parameters on computational efficiency and accuracy.

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^☆: Presented at the lecture series on “Applications and methods of random data analysis” on 8 to 11 July 1969, at Southampton University.

^‡: At present on leave at Department of Mathematics, Imperial College of Science and Technology, London, England.

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The fast Fourier transform algorithm: Programming considerations in the calculation of sine, cosine and Laplace transforms☆

Abstract

An algorithm for the machine calculation of complex Fourier series

Maths Comput.

What is the fast Fourier transform?

Historical notes on the fast Fourier transform

Application of the fast Fourier transform to computation of Fourier integrals, Fourier series, and convolution integrals

IEEE Trans. Audio Electroacoust.

The discrete Fourier transform

IBM Watson Research Center, Yorktown Heights, New York, RC2285

The discrete Fourier Transform?

IEEE Trans Audio Electroacoust