关于信号正交分解在Fourier变换中的几点思考  

Aspects of Signal Orthogonal Decompose in Fourier Transform

作　　者：杨永红[1] 张尤赛[1] 戴亮[1] 

机构地区：[1]江苏科技大学电子与信息学院,江苏镇江212003

出　　处：《电气电子教学学报》2009年第6期110-111,共2页Journal of Electrical and Electronic Education

摘　　要：在"信号与系统"课程中,Fourier变换和Fourier级数这一教学难点,强调了学习信号正交分解这一理论基础的必要性。本文首先阐述了正交、正交函数集以及完备正交函数集的概念,并进行了深入的探讨。在最小均方误差准则下,推导了信号正交分解的表达式;并得到了一个有用的推论,即帕塞瓦尔定理。该定理表明在正交函数集下,各个分量信号的能量之和与原信号的能量相等。最后,本文以方波作为仿真实例来加以说明和验证。Aiming at the difficulty of Fourier transform and Fourier series, we emphasis on the theoretical importance of studying the signal orthogonal decomposing, whieh meet with teach the course of signal and system. In this paper, we describe the conception of orthicon, orthogonal function set and completion of orthogonal function set conception and compared to them. Under the guideline of minimum mean square error, we deduce the formulae of signal orthogonal decompose, and one useful deduction is obtained, which is named as Parseval theorem. The Parseval theorem is shown that the energy sums of components signal are equal to the raw signal. As {ar as square waves are concerned, simulations are given for explanations.

关 键 词：正交函数集 FOURIER变换 最小均方误差 

分 类 号：TN911[电子电信—通信与信息系统]