关于能量有限信号的正交函数分解

On the Decomposition Into Orthogonal Functions for Signal With Finite Energy

证明了若将信号用正交函数的线性组合表示,在误差能量为最小条件的条件下,其系数与通常的按均方误差最小所得的结果一致。若正交函数为复指数集,其系数正好是傅里叶系数。

It is proved that the coefficients in condition of minimal error energy are equal to the coefficients with minimal error of the average square when signal is expressed by linear combination of orthogonal functions. The coefficients are Fourier coefficients to the moment when the orthogonal functions are complex exponential functions.