128
Views
6
CrossRef citations to date
0
Altmetric
Articles

Discontinuous Fast Fourier Transform with Triangle Mesh for Two-dimensional Discontinuous Functions

, , &
Pages 1045-1057 | Published online: 03 Apr 2012

References

  • Lo , Y. T. and Lee , S. W. 1993 . Antenna Handbook, Vol II: Antenna Theory Van Nostrand Reinhold , Newyork
  • Hung , C. C. and Mittra , R. 1983 . Secondary pattern and focal region distribution of reflector antennas under wide-angle scanning . IEEE Trans. Antennas Propagat. , 31 ( No. 5 ) : 756 – 763 .
  • Leou , J. L. and Li , H. J. 2000 . Evaluation of bistatic far-field quantities from near-field measurements . Progress In Electromagnetics Research , 25 : 167 – 188 .
  • Liu , Y. H. , Liu , Q. H. and Nie , Z.-P. 2009 . A new efficient FDTD time-to-frequency-domain conversion algorithm . Progress In Electromagnetics Research , 92 : 33 – 46 .
  • Chen , C. Y. , Wu , Q. Bi , X. J. 2010 . Characteristic analysis for FDTD based on frequency response . Journal of Electromagnetic Waves and Applications , 24 ( No. 2–3 ) : 283 – 292 .
  • Fan , G.-X. and Liu , Q. H. 2001 . The CGFFT method with a discontinuous FFT algorithm . Microwave Opt. Technol. Lett. , 29 : 47 – 49 .
  • Zhu , A. and Gedney , S. D. 2003 . A quadrature-sampled precorrected FFT method for the electromagnetic scattering from inhomogeneous objects . IEEE Antennas Wireless Propagat. Lett. , 2 : 50 – 53 .
  • Fan , Z. , Chen , R.-S. , Chen , H. and Ding , D.-Z. 2009 . Weak form nonuniform fast Fourier transform method for solving volume integral equations . Progress In Electromagnetics Research , 89 : 275 – 289 .
  • Semnani , A. and Kamyab , M. 2008 . Truncated cosine Fourier series expansion method for solving 2-D inverse scattering problems . Progress In Electromagnetics Research , 81 : 73 – 97 .
  • Huang , Y. , Liu , Y. , Liu , Q. H. and Zhang , J. 2010 . Improved 3-D GPR detection by NUFFT combined with MPD method . Progress In Electromagnetics Research , 103 : 185 – 199 .
  • Sorets , E. 1995 . Fast Fourier transforms of piecewise constant function . J. Comput. Phys. , 116 : 369 – 379 .
  • Fan , G.-X. and Liu , Q. H. 2004 . Fast Fourier transform for discontinuous functions . IEEE Trans. Antennas Propagat. , 52 : 461 – 465 .
  • Liu , Y.-H , Nie , Z.-P. and Liu , Q. H. 2008 . A fast and accurate algorithm for Fourier transform integrals of discontinuous functions . IEEE Microwave and Wireless Components Lett. , 18 ( No. 11 ) : 716 – 718 .
  • Zhu , C.-H. , Liu , Q. H. , Shen , Y. and Liu , L. 2010 . A high accuracy conformal method for evaluating the discontinuous Fourier transform . Progress In Electromagnetics Research , 109 : 425 – 440 .
  • Cowper , G. R. 1973 . Gaussian quadrature formulas for triangles . Int. J. Numer. Methods Eng. , 7 ( No. 3 ) : 405 – 408 .
  • Liu , Q. H. and Nguyen , N. 1998 . An accurate algorithm for nonuniform fast Fourier transform (NUFFT’s) . IEEE Microwave and Guided Wave Lett. , 8 ( No. 1 ) : 18 – 20 .
  • Nguyen , N. and Liu , Q. H. 1999 . The regular Fourier matrices and nonuniform fast Fouirer transforms . SIAM J. Sci. Comput. , 21 ( No. 1 ) : 283 – 293 .
  • Song , J.-Y. , Liu , Y.-H. Gewalt , S. L. 2009 . Least-square NUFFT methods applied to 2D and 3D radially encoded MR image reconstruction . IEEE Transaction on Biomedical Engineering , 56 ( No. 4 ) : 1134 – 1142 .
  • Dutt , A. and Rokhlin , V. 1993 . Fast Fourier transforms for nonequispaced data . SIAM J. Sci. Comp. , 14 : 1368 – 1393 .
  • Fessler , J. A. and Sutton , B. P. 2003 . Nonuniform fast Fourier transform using min-max interpolation . IEEE Trans. Signal Process. , 51 : 560 – 574 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.