## Geometric interpretations of the discrete Fourier transform (dft)C. Warren Campbell, United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1984 - Mathematics - 11 pages |

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2Af 3Af 4Af 3Af 2Af 3Af 4Af 3Af apparent complexity axis points Carlo turbulence simulation complex conjugate pairs continuous Fourier transform coordinate axis coordinate direc Correspondence of complex defined by equations dfl df2 DFTs OF REAL dimensions the DFT direct correspondence Discrete Fourier Transform dt2 dt3 dtl dt2 exp j27r(fltl exp j27rnk/N Extension to higher Fast Fourier Transform FFT storage strategy Figure Fourier Transform DFT Fourier Transform periodicity frequency domain Geometric Interpretations given by equation Hermitian symmetry higher dimensions interior real point Marshall Space Flight Monte Carlo turbulence move two sub-blocks N/2nd point NASA negative frequency axis normal FFT storage one-dimensional DFT one-dimensional transform domain oo oo oo PERFORMING ORGANIZATION positive frequencies quadrant N1/2+1 real function rearranged DFT reflection principle sampling frequency sided continuous Fourier Space Flight Center space is filled SYMMETRY PROPERTIES three dimensions Three-dimensional DFT storage two-dimensional transform domain two-sided continuous Fourier two-sided continuous transform Warren Campbell Xc(kAf