为了知道信号能量或功率的特性，常常研究信号(电流或电压)在一单位电阻上所消耗的能量或功率。信号http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181812820.gif内能量为

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181812388.gif

在区间http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181812333.gif内的平均功率为

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181812764.gif

信号的能量定义为在时间区间http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181812507.gif的能量，记为

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181812799.gif

信号的功率定义为在时间区间http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181812797.gif的平均功率，记为

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181812672.gif

1.能量信号

若信号http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181813422.gif的能量为有限值，即

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181813351.gif)

则信号http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181813980.gif等。

2.功率信号

若信号http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181813972.gif的功率为有限值，即

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181813657.gif)

则信号http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181813404.gif等。

此外，还有一些非功率非能量的信号，例单位斜坡信号http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181813410.gif等。

二、功率频谱

对于周期信号http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181813896.gif，因

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181814967.gif

由式(3-29)可知

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181814573.gif

所以对周期信号可以用功率振幅频谱描述其功率的频率特性。

对于非周期功率信号，可定义一个功率密度函数http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181814164.gif，即单位频率的信号功率。从而信号的总功率为

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181814701.gif

若信号http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181814961.gif，则由帕塞瓦尔定理

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181814375.gif

可知

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181814542.gif

比较式(3-86)和式(3-87)，有

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181814910.gif

所以对于非周期功率信号可用功率密度函数http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181814485.gif的偶函数，它仅取决于频谱函数的模量，而与相位无关，单位为瓦·秒 (http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181814768.gif)。

对于周期信号，很容易求得其功率谱:

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181814790.gif。

三、能量频谱

对于能量信号，同样可用密度的概念表示信号能量在各频率点的分布情况，即定义单位频率内的信号能量为能量密度函数，记为http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181815962.gif的总能量为

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181815498.gif

若信号f(t)的频谱函数为F(jω)，由帕塞瓦尔定理，有

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181815959.gif

因此

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181815504.gif

故对于能量信号可用能量密度函数http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181815475.gif)。

由以上讨论可知，信号的功率或能量既可在时域内求得，也可以在频域内求得。它反映能量守恒定理在信号分析中的体现，也是信号的时域特性与频域特性的一个重要关系。

例3-21 求信号

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181815597.gif

的能量。

解: 由式(3-54)可知，对于单位矩形脉冲信号

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181815681.gif

当http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181815879.gif时，

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181815310.gif

根据傅里叶变换对称性，有

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181815891.gif

有

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181815706.gif

又

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181816932.gif

所以，利用频域卷积定理，得

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181816847.gif

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181816524.gif

故信号的能量为

http://www.61ic.com/Technology/UploadFiles_8326/201103/20110331181816971.gif