期刊
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
卷 52, 期 2, 页码 461-465出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAP.2004.823965
关键词
discontinuous fast Fourier transform (DFFT); algorithm; discontinuous function; fast Fourier transform (FFT); Fourier transform; interpolation; nonuniform FFT (NUFFT); spectral method
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(vNp + vN log (N)) where p is the interpolation order and v 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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