A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformatio...A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformations in the wavenumber domain, which not only gives a more flexible algorithm of potential field transformations, but also reveals the law of error of potential field transformations in the wavenumber domain. The DFT0η η（0.5, 0.5） reduction-to-pole （RTP） technique derived from the A-E equation significantly improves the resolution and accuracy of RTP anomalies at low magnetic latitudes, including the magnetic equator. The law （origin, form mechanism, and essential properties） of the edge oscillation revealed by the A-E equation points out theoretically a way of improving the effect of existing padding methods in high-pass transformations in the wavenumber domain.展开更多
The DFT transform us 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 (DFT...The DFT transform us 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.展开更多
文摘A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformations in the wavenumber domain, which not only gives a more flexible algorithm of potential field transformations, but also reveals the law of error of potential field transformations in the wavenumber domain. The DFT0η η（0.5, 0.5） reduction-to-pole （RTP） technique derived from the A-E equation significantly improves the resolution and accuracy of RTP anomalies at low magnetic latitudes, including the magnetic equator. The law （origin, form mechanism, and essential properties） of the edge oscillation revealed by the A-E equation points out theoretically a way of improving the effect of existing padding methods in high-pass transformations in the wavenumber domain.
文摘The DFT transform us 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.
