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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2-D Fast Fourier 2Af 3Af 3Af 4Af 3Af 4Af 3Af 2Af apparent complexity axis points Carlo turbulence simulation complex conjugate pairs continuous and digital continuous Fourier transform coordinate axis coordinate direc Correspondence of complex defined by equations depicts dfl df2 DFTs OF REAL dimensions are obvious dimensions the DFT direct correspondence DISCRETE FOURIER TRANSFORM dt2 dt3 dtl dt2 exp j27r(nlkl/Nl exp j27rnk/N exp j2ir(fltl Fast Fourier Transform FFT storage strategy Figure Fourier space Fourier Transform periodicity frequency domain GEOMETRIC INTERPRETATIONS given by equation Hermitian symmetry higher dimensions interior real point Monte Carlo turbulence move two sub-blocks N/2nd point NASA negative frequency axis normal FFT storage one-dimensional DFT One-Dimensional Symmetry one-dimensional transform domain positive frequencies quadrant N1/2+1 real function rearranged DFT reflection principle sampling frequency sided continuous Fourier space is filled three dimensions Three-dimensional DFT storage two-dimensional DFT two-dimensional transform domain two-sided continuous Fourier two-sided continuous transform Xc(kAf xc(nAt