DFTS on irregular grids
Subtitle: the anterpolated DFT
By: by Van Emden Henson
Contributors: Naval Postgraduate School (U.S.). Dept. of Mathematics
Publisher: Naval Postgraduate School; Available from National Technical Information Service
Published: 1992
Place of publication: Monterey, Calif; Springfield, Va
Language: eng
Number of pages: 14
Subjects: FAST FOURIER TRANSFORMS; DISCRETE FOURIER TRANSFORMS
Other titles: NPS-MA-92-006.
Description: In many instances the discrete Fourier transform (DFT) is desired for a data set that      occurs on an irregular grid. Commonly the data are interpolated to a regular grid, and a      fast Fourier transform (FFT) is then applied. A drawback to this approach is that typically      the data have unknown smoothness properties, so that the error in the interpolation is      unknown. An alternative method is presented, based upon multilevel integration techniques      introduced by A. Brandt. In this approach, the kernel, e(-iwt), is interpolated to the      irregular grid, rather than interpolating the data to the regular grid. This may be      accomplished by pre-multiplying the data by the adjoint of the interpolation matrix (a      process dubbed anterpolation), producing a new regular-grid function, and then applying a      standard FFT to the new function. Since the kernel is C infinity the operation may be      carried out to any preselected accuracy. A simple optimization problem can be solved to      select the problem parameters in an efficient way. If the requirements of accuracy are not      strict, or if a small bandwidth is of interest, the method can be used in place of an FFT      even when the data are regularly spaced. Discrete Fourier Transform, FFT, Anterpolation.
Notes: Title from cover.

"NPS-MA-92-006."

"Technical report for period October 1990-March 1992."

AD A255 187.

Includes bibliographical references (p. 11-12)

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