从正交分解看傅里叶级数

Comprehending Fourier Series through Orthogonal Decomposition

基于正交的概念,指出了三角函数系的正交性、完备性;从正交分解的角度理解将一个周期函数展开成傅里叶级数;从函数做正交分解时系数的确定方法理解傅里叶系数.

This article summarizes theorthogonality and completeness of trigonometric function system based on the concept of the orthogonality, explains the Fourier expansion of a periodic function from the view point of orthogonal decomposition, and understands themeaning of Fourier coefficients by the orthog-onal decomposition process.