周期序列正交分解和离散傅里叶级数

本文试图用信号线性逼近的方法和正交分解的理论导出周期序列离散傅里叶级数DFS关系式。推导过程表明,在N维序列空间上,用N维复指数序列集线性逼近任一周期序列,在方均误差最小的条件下,其表达式就是DFS关系式;同时说明,周期序列的DFS部分展开式在方均误差准则下线性逼近误差最小。

Orthogonal Decomposition of Periodic Sequences and Discrete Fourier Series

In this paper the expression of discrete Fourier series(DFS) for periodic sequences has been deduced from periodic sequence linear approximation and orthogonal decomposition. The deduction shows that in the periodic sequenc space, when a set of N-di ensional co plex exponent sequences is used to approach linearly to any periodic sequence, the result under the condition of the minimum mean square error is just the expression of the DFS, and that expanded expression of part of DFS of a periodic sequence will have a minimum error if it is used to approach the sequence.