数字信号处理－ chap2 数字信号

爱被打了一巴掌 2021-11-04 11:08 533阅读 0赞

## 1. 图形表示 ##

数字信号基本为模型信号按一定间隔进行采样，经过模式转换得到。它用顶部带圆圈的竖线表示。

> 1）横坐标：每条线表示一个采样点，并用一整数标记，这个整数是所经过的采样周期的数目。
> 
> 2）纵坐标：数字信号值是A/D转换时最解决该模拟采样值的量化电平。

[![image][]][image 1]

## 2.符号表示 ##

数字信号x用符号表示为x\[n\]，n是采样编号。

> 1）时移：x\[n-N\]表示右移N个采样点
> 
> 2）尺度变换:x\[kn\]从信号中选取第k个采样点

## 3.数字函数 ##

### 3.1脉冲函数 ###

脉冲函数又称（[![image][image 2]][image_image 2] 函数）

[![image][image 3]][image_image 3] [![image][image 4]][image_image 4]

脉冲函数是基本函数，所有数字信号都能从它构造出来。**任何函数都能写为脉冲函数之和的形式**

[![image][image 5]][image_image 5] ，其中[![image][image 6]][image_image 6] 是采样值

### 3.2 阶跃函数 ###

阶跃函数常用来表示一个接通过程。

[![image][image 7]][image_image 7] [![image][image 8]][image_image 8]

阶跃函数可表示为脉冲函数之和

[![image][image 9]][image_image 9]

脉冲函数可表示为阶跃函数之差

[![image][image 10]][image_image 10]

### 3.3 幂函数和指数函数 ###

幂函数：[![image][image 11]][image_image 11]

指数函数：[![image][image 12]][image_image 12]

### 3.4 正弦和余弦函数 ###

定义为：

[![image][image 13]][image_image 13] （1）

A是振幅，[![image][image 14]][image_image 14] 是数字序列重复的频率。

**注意：不同于模型信号，数字正弦和余弦不一定是周期的，**[**![image][image 15]**][image_image 15] **也不等于被采样模拟信号的频率。**

**由模拟频率与数字频率间的关系建立过程如下：**

> 1）模拟正弦[![image][image 16]][image_image 16] ，[![image][image 17]][image_image 17] 为频率，单位为弧度/秒。信号在每个时刻t都有值。
> 
> 2）采样：每Ts秒采样一次，采样时间表示为t=nTs。因此，模拟域中采样值表示为x(nTs)，数字域中表示为x\[n\]，忽略量化误差有
> 
> [![image][image 18]][image_image 18] （2）
> 
> 且在时刻nTs，模拟信号值为
> 
> [![image][image 19]][image_image 19] （3）
> 
> 3）变换：由于[![image][image 20]][image_image 20] ；Ts=1/*fs*，*fs*是采样频率，带入（3）有
> 
> [![image][image 21]][image_image 21] （4）
> 
> 4）建立联系：由式（2），令式（4）等于式（1）有
> 
> [![image][image 22]][image_image 22] （5）
> 
> 从而得到 [![image][image 23]][image_image 23] （6）
> 
> **注：式（6）将数字频率**[**![image][image 14]**][image_image 14]**与模拟频率*f*联系起来**。数字频率的单位是弧度，而不是弧度/秒，因为数字域中经过的时间用采样个数度量，而不是秒。

转载于:https://www.cnblogs.com/pegasus/archive/2011/02/15/1955557.html

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