Fourier Analysis

Transforms provide an alternative representation of images, which usually facilitates easier interpretation of operations and fast processing. The most important of all the transforms, the Fourier transform, decomposes an image in terms of sinusoidal surfaces. This transform is of fundamental importance in image processing, as is the case in almost all areas of science and engineering. As in the case of the convolution operation, both the 1-D and 2-D versions are described. Although the image is a 2-D signal, some of the important operations are decomposable and can be carried out in one dimension with reduced execution time. Another advantage is that understanding of the 1-D version is simpler. Definition, properties and examples of the transform are presented.