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.
U. Martin Skrodzki, and K. Polthier. Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture, page 481--484. Phoenix, Arizona, Tessellations Publishing, (2016)Available online at http://archive.bridgesmathart.org/2016/bridges2016-481.html.
M. Raginsky, and I. Sason. (2012)cite arxiv:1212.4663Comment: Foundations and Trends in Communications and Information Theory, vol. 10, no 1-2, pp. 1-248, 2013. Second edition was published in October 2014. ISBN to printed book: 978-1-60198-906-2.