Some Eigenfunction Methods for Computing a Numerical Fourier Transform
- 1 December 1976
- journal article
- research article
- Published by Oxford University Press (OUP) in IMA Journal of Applied Mathematics
- Vol. 18 (3) , 279-293
- https://doi.org/10.1093/imamat/18.3.279
Abstract
A number of methods for calculating the Fourier transform of a function given numerically are studied. These methods exploit the fact that the Hermite functions are eigen-functions of the Fourier transform. The transforms of four types of functions are considered: (i) functions of the form p(x) exp (−x2/2), where p(x) is a polynomial, (ii) functions with bounded support. (iii) rapidly decreasing functions, and (iv) functions whose transform has bounded support. In each case algorithms for calculating the transformed function are derived. Error estimates are made in two of the cases and results of numerical experiments presented in an appendix.Keywords
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