By Topic

Fast Fourier transform of sparse spatial data to sparse Fourier data

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Chew, W.C. ; Dept. of Electr. & Comput. Eng., Illinois Univ., Urbana, IL, USA ; Song, J.M.

The nonuniform fast Fourier transform (FFT) on a line has been of interest to a number of scientists for its practical applications. However, not much has been written on Fourier transforming sparse spatial data where the Fourier transform is needed at only sparse data points in the Fourier space in 2D or 3D. It finds applications in remote sensing, inverse problems, and synthetic aperture radar where the scattered field is related to the Fourier transform of the scatterers. We outline an algorithm to perform this transform in NlogN operations, where N is the number of spatial data available, and we assume that the number of Fourier data desired is also of O(N). The algorithm described here is motivated by the multilevel fast multipole algorithm (MLFMA), but is different from that described by Brandt (1991). In MLFMA, an embedded fast Fourier transform algorithm is inherent, where the spatial data is arbitrarily distributed, but the Fourier data is required on the Ewald sphere. In the present algorithm, the restriction of the Fourier data to an Ewald sphere is lifted so that it can be arbitrarily distributed as well. The present algorithm can be easily generalized to 3D.

Published in:

Antennas and Propagation Society International Symposium, 2000. IEEE  (Volume:4 )

Date of Conference:

16-21 July 2000