ABSTRACT
In image processing, one often encounters the problem of filtering an image in order to suppress some of its features while enhancing others. Fourier analysis is a well-known technique of spectral analysis using trigonometric functions of various periods to represent functions at various scales. The techniques of Fourier analysis are powerful and find wide-ranging applications not only in the mathematical sciences but also within pure mathematics. From a statistical point of view, obtaining the Fourier spectrum of a function is the same as obtaining the least square fit of sines and cosines of various frequencies in one or more dimensions. Multiple regression using trigonometric functions is very elegant and simple, since the trigonometric sines and cosines are mutually orthonormal, and the coefficients of regression are written as simple sums of products or as integrals of products of functions.
