Fundamental Properties of 2D DFT 

The 2D FT can be implemented as two consecutive 1D FTs: first in the x direction, then in the y direction (or vice versa). Symbolically:
The computation of the 2D Fourier transform as a series of 1D transforms. [More] The FT of a shifted function is unaltered except for a linearly varying phase factor. [More]
The DFT and IDFT are periodic with period N ; that is:
[More] Simply stated: if a function is rotated, then its Fourier transform rotates an equal amount.
[More] The Fourier transform and its inverse are distributive over addition but not over multiplication.
This property is best summarized by "a contraction in one domain produces corresponding expansion in the Fourier domain".
The convolution of two functions f(x) and g(x) is defined by the integral:
The Convolution Theorem
tells us that convolution in the spatial domain corresponds to
multiplication in the frequency domain, and vice versa.
[More] One of the principal applications of correlation in image processing is in the area of template or prototype matching i.e. finding the closest match between an unknown image and a set of known images.
[More] Again this is a property which has no useful analogy in one dimension. The theorem can be stated briefly: the (1D) Fourier transform of the projection of a 2D function is the central slice of the Fourier transform of that function.
If F(u,0) is the central slice, and defines the projection of f(x,y) on the x axis then:

