Finite Fourier series

摘要

Fourier series and transforms, which express a continuous function in an alternative form through nearly self-reciprocal transformations, can be extended to a finite set of points. Modular parts, a generalization of even and odd parts of a function, can be defined in terms of finite Fourier series. A means of radiating or dispersing modular parts is derived using nonreal square roots of + 1.