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2D discrete Fourier transform

A complex value F(u,v) for every row-frequency/column-frequency pair, computed from every pixel.

The 2D discrete Fourier transform of an H\times W image f(x,y) is F(u,v) = \sum_{x=0}^{H-1}\sum_{y=0}^{W-1} f(x,y)\, e^{-j2\pi(ux/H+vy/W)}, a full H\times W grid of complex numbers carrying exactly the same information as the original image, just organized by frequency instead of by position -- reversible via the inverse DFT.

See also

magnitude spectrum phase spectrum
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