For what is an image, after all? What is a mathematical description of an image? Well, at least not a two-dimensional image. At least mathematically, it's given by a function of two variables, say X1 and X2. Function F of X1, X2, where X1 and X2 are varying over some part of the X1, X2 plane. At each point, what the function prescribes is the intensity. I'm thinking about black and white images here. So you think F of X1 and X2 as a range of numbers from zero to one, from black to white. So you think of F of X1, X2 as the intensity from black to white, say, at the point X1, X2. ...

See the whole transcript at The Fourier Transform and its Applications - Lecture 26