Shift sampling theory of Fourier transform computation

The DFT transform is extended to DFTepsilon eta transform and the relationship between FT and DFTepsilon eta is given by the Fourier transform discretization theorem. Based on the theorem, the DFTepsilon eta algorithm-error equation (DFT(epsilon eta)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.