Abstract
The DFT transform is extended to DFTξη transform and the relationship between FT and DFTξη is given by the Fourier transform discretization theorem. Based on the theorem, the DFTξη algorithm-error equation (DFTξη A-E equation) is established, and the minimization property of discrete effect and the oscillation property of truncation effect are demonstrated. All these construct the shift sampling theory—a new theory about Fourier transform computation.
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Chai, Y. Shift sampling theory of Fourier transform computation. Sci. China Ser. E-Technol. Sci. 40, 21–27 (1997). https://doi.org/10.1007/BF02916587
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DOI: https://doi.org/10.1007/BF02916587