Eigenfunctions of the Fourier transformation over a circle — I – Approximation of Sturmian eigenvalues

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Authors
  1. Boivin, R.F.
Corporate Authors
Defence R&D Canada - Ottawa, Ottawa ONT (CAN)
Abstract
We clarify and expand upon Slepian's perturbation scheme for approximating the eigenvalues of the Sturm-Liouville equation characterizing the eigenfunctions of the finite Fourier transformation over a circle. The eigenvalues are approximated as power series in terms of c² or 1/c, where c represents the adjustable scaling constant that controls mapping of the frequency domain of the transformation to the field domain. Analytical expressions of the series coefficients are worked out up to fifth order. An algorithm is also provided for numerical determination of higher-order coefficients. The accuracy of the series is investigated; prospects for extensive computations of the eigenvalue spectrum are discussed; and some applications of the eigenfunctions are outlined.

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Report Number
DRDC-OTTAWA-TM-2008-342 — Technical Memorandum
Date of publication
01 Mar 2009
Number of Pages
106
DSTKIM No
CA032273
CANDIS No
531365
Format(s):
CD ROM

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