Fourier theory is pretty complicated mathematically. But there are some beautifully simple holistic concepts behind Fourier theory which are relatively easy to explain intuitively. There are other sites on the web that can give you the mathematical formulation of the Fourier transform. I will present only the basic intuitive insights here, as applied to spatial imagery.
M. Mariotti. Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education, 1, page 180--195. Stellenbosch, South Africa, PME, University of Stellenbosch, (July 1998)