| Publications [#283629] of Qing H. Liu
Papers Published
- Fan, GX; Liu, QH, Fast Fourier transform for discontinuous functions,
Ieee Transactions on Antennas and Propagation, vol. 52 no. 2
(February, 2004),
pp. 461-465, Institute of Electrical and Electronics Engineers (IEEE) [doi]
(last updated on 2023/08/08)
Abstract: 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 + νN log (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.
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