Affine theorem for two-dimensional Fourier transform

Abstract

The well known shift and similarity theorems for the Fourier transform generalise to two dimensions but new theorems come into existence in two dimensions. Simple theorems for rotation and shear distortion are examples. A theorem is presented which determines what the Fourier transform becomes when the function domain is subjected to an affine co-ordinate transformation. The full theorem contains a variety of simpler theorems as special cases. It may prove useful in its general form in image processing where sequences of affine transformations are applied.