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Fast Fourier transform for discontinuous functions

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2 Author(s)
Guo-Xin Fan ; Dept. of Electr. & Comput. Eng., Duke Univ., Durham, NC, USA ; Qing Huo Liu

In computational electromagnetics and other areas of computational science and engineering, Fourier transforms of discontinuous functions are often required. We present a fast algorithm for the evaluation of the Fourier transform of piecewise smooth functions with uniformly or nonuniformly sampled data by using a double interpolation procedure combined with the fast Fourier transform (FFT) algorithm. We call this the discontinuous FFT algorithm. For N sample points, the complexity of the algorithm is O(νNp+νNlog(N)) where p is the interpolation order and ν is the oversampling factor. The method also provides a new nonuniform FFT algorithm for continuous functions. Numerical experiments demonstrate the high efficiency and accuracy of this discontinuous FFT algorithm.

Published in:

Antennas and Propagation, IEEE Transactions on  (Volume:52 ,  Issue: 2 )