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Next: The Discrete Fourier Transform Up: Fourier Theory Previous: 1D Case

2D Case

If f(x,y) is a function, for example the brightness in an image, its Fourier transform is given by
F(u,v) = \int_{-\infty}^\infty\int_{-\infty}^\infty f(x,y) 
e^{-2\pi i (x u+y v)}\,dx\,dy, \end{displaymath} (4)
and the inverse transform, as might be expected, is
f(x,y) = \int_{-\infty}^\infty\int_{-\infty}^\infty F(u,v) e^{2\pi
i (x u+y v)}\,du\,dv. \end{displaymath} (5)

Dave Marshall