At top consider the data point and frequency coefficient <b>locations</b> for a 1D N=2<sup>3</sup>=8 discrete transform in direct and reciprocal space. A bar denotes a negative value, a dot denotes a ± value, and red coefficients are "self-conjugate" (hence real) when a real starting array requires conjugate symmetry in the Fourier transform. 
<p>Below that we show the same location set for a 2D N=2<sup>2</sup> or 4×4 discrete Fourier transform, moving first from coordinate space to frequency space, and from there to the "rotated" or shifted frequency space view which better reflects the range symmetry as well as the diffraction symmetry of power spectra. 
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At bottom, compare data point and coefficient locations for a 2D N=2<sup>3</sup> or 8×8 discrete Fourier transform. In all cases for these discrete transforms, periodic boundary conditions are assumed and frequencies are in cycles (not radians) per unit time or distance.
<a href="//commons.wikimedia.org/wiki/User:Unitsphere" title="User:Unitsphere">P. Fraundorf</a>
CC BY-SA 4.0
<span class="int-own-work" lang="en">Own work</span>