计算机应用 | 古代文学 | 市场营销 | 生命科学 | 交通物流 | 财务管理 | 历史学 | 毕业 | 哲学 | 政治 | 财税 | 经济 | 金融 | 审计 | 法学 | 护理学 | 国际经济与贸易
计算机软件 | 新闻传播 | 电子商务 | 土木工程 | 临床医学 | 旅游管理 | 建筑学 | 文学 | 化学 | 数学 | 物理 | 地理 | 理工 | 生命 | 文化 | 企业管理 | 电子信息工程
计算机网络 | 语言文学 | 信息安全 | 工程力学 | 工商管理 | 经济管理 | 计算机 | 机电 | 材料 | 医学 | 药学 | 会计 | 硕士 | 法律 | MBA
现当代文学 | 英美文学 | 通讯工程 | 网络工程 | 行政管理 | 公共管理 | 自动化 | 艺术 | 音乐 | 舞蹈 | 美术 | 本科 | 教育 | 英语 |

“免费”FIR数字滤波器的MATLAB实现(一)-通信工程

2013-06-27 01:15
导读：通信工程论文毕业论文，“免费”FIR数字滤波器的MATLAB实现(一)-通信工程样式参考，免费教你怎么写，格式要求，科教论文网提供大量范文样本：

FIR数字滤波器的MATLAB实现

 

 

1．FIR数字滤波器的基本结构

 

一个数字滤波器可以用系统函数表示为

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-22618.png" width="198" height="89" />                     （1.1.1）

 

直接由此式可得出表示输入输出关系的常系数线性差分方程为

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-28576.png" width="254" height="46" />              （1.1.2）

 

可以看出，数字滤波器的功能就是把输入序列通过一定的运算变换成输出序列。

 

有限长单位冲激响应（FIR）滤波器有以下几个特点：

 

（1） 系统的单位冲激响应h(n)在有限个n值处不为零；

 

（2） 系统函数H(z)在︱z︱>0处只有零点，有限z平面只有零点，而全部极点都在z=0处（因果系统）；

 

（3） 结构上主要是非递归结构，没有输出到输入的反馈，但有些结构中（例如频率抽样结构）也包含有反馈的递归部分。

 

设FIR滤波器的单位冲激响应h(n)为一个N点序列，600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-22304.png" width="89" height="19" />，则滤波器的系统函数为

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-16086.png" width="133" height="46" />                             （1.1.3）

 

就是说，它有（N-1）阶极点在z=0处，有（N-1）个零点位于有限z平面的任何位置。FIR滤波器有以下几种基本结构。

 

 

1.1．横截型（卷积型、直接型）

 

    系统的差分方程表达式为

 

              600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-31365.png" width="173" height="46" />                        （1.1.4）

 

很明显，这就是线性移不变系统的卷积和公式，也是x(n)的延时链的横向结构，如下图所示

 

 

 

 

  x(n)        600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-18097.png" width="23" height="21" />      600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7537.png" width="23" height="21" />                   600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-31896.png" width="23" height="21" />

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-13667.png" width="97" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-18161.png" width="9" height="63" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-25190.png" width="61" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-21465.png" width="61" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-22395.png" width="9" height="63" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-6743.png" width="9" height="63" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-10089.png" width="9" height="63" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-8480.png" width="9" height="63" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-21114.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-9.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-13499.png" width="25" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-6134.png" width="25" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-8604.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-26313.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-13234.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-12890.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-5673.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23449.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-18465.png" width="61" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23983.png" width="61" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-5765.png" width="61" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7864.png" width="61" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-20588.png" width="61" height="9" />

 

        h(0)    h(1)    h(2)        h(N-2)           h(N-1)

 

                                                                y(n)

 

 

                   图1.1.1 FIR滤波器的横截型结构

 

1.2．级联型

 

将H(z)分解成实系数二阶因子的乘积形式

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-29973.png" width="330" height="58" />        （1.2.1）

 

其中600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-20411.png" width="31" height="42" />表示取N/2的整数部分。若N为偶数，则N-1为奇数，故系数600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-17428.png" width="27" height="25" />中有一个为零。这是因为有奇数个根，其中复数根成共轭对，必为偶数，必然有奇数个实根。

 

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-32666.png" width="9" height="53" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-21255.png" width="9" height="63" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-6065.png" width="97" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23054.png" width="97" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-14934.png" width="9" height="53" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23060.png" width="9" height="63" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-21769.png" width="9" height="63" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-16848.png" width="9" height="53" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-24051.png" width="85" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-22621.png" width="85" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7400.png" width="9" height="53" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7381.png" width="9" height="63" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-8912.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-22024.png" width="85" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-10649.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-28968.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-30179.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-12013.png" width="85" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-25042.png" width="85" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-21509.png" width="9" height="53" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-11766.png" width="9" height="63" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23290.png" width="73" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-32282.png" width="73" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-17960.png" width="9" height="53" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-2530.png" width="9" height="63" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-6771.png" width="73" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-1840.png" width="73" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-4255.png" width="73" height="9" /> x(n)        600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-17550.png" width="25" height="25" />                600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-14969.png" width="26" height="25" />                 600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23619.png" width="37" height="38" />          y(n)

 

      600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-560.png" width="23" height="21" />    600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-27837.png" width="25" height="23" />        600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23949.png" width="23" height="21" />    600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-26981.png" width="25" height="23" />          600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7157.png" width="23" height="21" />     600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-28458.png" width="35" height="38" />

 

      

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-11600.png" width="23" height="21" />     600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-8766.png" width="25" height="23" />       600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-29001.png" width="23" height="21" />     600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-1751.png" width="26" height="23" />         600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-22924.png" width="23" height="21" />      600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-5373.png" width="38" height="38" />

 

 

          图1.2.1 FIR滤波器的级联型结构（N为奇数）

 

这种结构的每一节控制一对零点，因而在需控制传输零点时，可以用它。但是这种结构所需的系数600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-16104.png" width="23" height="25" />（i=0,1,2;k=1,2,…,[N/2]比卷积型的系数h(n)要多，因此所需的乘法次数也比卷积型的要多。

 

1.3．频率抽样型

 

把一个N点有限长序列的z变换H(z)在单位圆上作N等份抽样，就得到600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-1954.png" width="39" height="33" />，其主值序列就等于h(n)的离散傅立叶变换H(k)。用H(k)表示H(z)的内插公式为

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-2168.png" width="13" height="23" />      600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-10644.png" width="221" height="47" />                       （1.3.1）

 

其中级联的第一部分为

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-32081.png" width="45" height="25" />=600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-14105.png" width="49" height="21" />                                       （1.3.2）

 

这是一个FIR子系统，是由N节延时单元构成的梳状滤波器，令

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7224.png" width="45" height="25" />=600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-24869.png" width="49" height="21" />=0

 

则有

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-29295.png" width="90" height="26" />

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-10127.png" width="65" height="38" />，  600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-29092.png" width="23" height="18" />0，1，…,N-1

 

即600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-10679.png" width="45" height="25" />在单位圆上有N个等间隔角度的零点，它的频率响应为

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-1657.png" width="255" height="46" />                  （1.3.3）

 

因而幅度响应为

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-18800.png" width="163" height="46" />

 

相角为

 

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-31818.png" width="37" height="137" />                              600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-6702.png" width="122" height="42" />

 

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-24599.png" width="201" height="42" />     600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-9937.png" width="134" height="42" />

 

                              …

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-25526.png" width="198" height="42" />

 

其子网络结构及频率响应幅度如图1-3所示。

 

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-10874.png" width="109" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-3014.png" width="2" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-32075.png" width="2" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-1521.png" width="133" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-15374.png" width="121" height="9" />       x(n)                                            y(n)

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-12925.png" width="133" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-10762.png" width="97" height="23" />                 600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-839.png" width="41" height="21" /> 

 

                        图1.3.1 梳状滤波器结构

 

级联的第二部分为

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-1684.png" width="171" height="47" />

 

它是由N个一阶网络并联组成，而这每一个一阶网络都是一个谐振器

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-9105.png" width="133" height="46" />                             （1.3.4）

 

令600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7201.png" width="46" height="26" />的分母为零，即令

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-14157.png" width="98" height="26" />

 

可得到此一阶网络在单位圆上有一个极点

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-15583.png" width="115" height="38" />

 

也就是说，此一阶网络在频率为

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-13782.png" width="65" height="42" />

 

处响应为无穷大，故等于谐振频率为600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-16672.png" width="37" height="42" />的无损耗谐振器。这个谐振器正好于与梳状滤波器的一个零点(i=k)相抵消，从而使这个频率（600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-17187.png" width="65" height="42" />）上的频率响应等于H(k)。这样，N个谐振器的N个极点就和梳状滤波器N个零点相互抵消，从而在N个频率抽样点（600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-32289.png" width="65" height="42" />，k=0,1,…,N-1）的频率响应就分别等于N个H(k)值。

 

N个并联谐振器与梳状滤波器级联后，就得到如图1-4的频率抽样结构。频率抽样结构的特点是它的系数H(k)就是滤波器在600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-17415.png" width="65" height="42" />处的响应，因此控制滤波器的频率响应很方便。但是结构中所乘的系数H(k)及600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-8169.png" width="33" height="26" />都是复数，增加了乘法次数和存储量，而且所有极点都在单位圆上，由系数600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-3319.png" width="33" height="26" />决定，这样，当系数量化时，这些极点会移动，有些极点就不能被梳状滤波器的零点所抵消（零点由延时单元决定，不受量化影响）。如果极点移到z平面单位圆外，系统就不稳定了[4]。

 

为了克服系数量化后可能不稳定的缺点，可以将频率抽样结构做一点修正，即将所有零、极点都移到单位圆内某一靠近单位圆、半径为r的圆上，使系统更加稳定。限于篇幅关系，这里就不作详细介绍。图1.3.2是未修正的频率抽样结构。

 

 

 

 

 

                                     

 

                                        H(0)

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-26462.png" width="2" height="22" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-22624.png" width="9" height="105" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-17305.png" width="9" height="53" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-25264.png" width="2" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-19226.png" width="2" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-25951.png" width="61" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-13762.png" width="145" height="9" />                                        600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-26041.png" width="23" height="21" />

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-13922.png" width="73" height="9" />                                        

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-5865.png" width="9" height="84" />                          600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-24894.png" width="50" height="26" />   H(1)

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-21553.png" width="2" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-1137.png" width="2" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-21706.png" width="61" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-29348.png" width="145" height="9" />   x(n)                                               1/N        

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-25196.png" width="2" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-27780.png" width="2" height="11" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-28965.png" width="2" height="11" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-30450.png" width="9" height="11" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-5866.png" width="2" height="11" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7574.png" width="2" height="11" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-9672.png" width="109" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-2239.png" width="2" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-15522.png" width="37" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23632.png" width="97" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-5683.png" width="73" height="9" />                                        600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-31985.png" width="23" height="21" />                 y(n)

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-11767.png" width="61" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-17370.png" width="2" height="11" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-15682.png" width="2" height="11" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23103.png" width="2" height="11" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-14779.png" width="2" height="11" />       -600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-4010.png" width="29" height="21" />                   600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-15850.png" width="75" height="38" />

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-15223.png" width="2" height="11" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-8340.png" width="2" height="11" />                                       H(N-1)

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-24157.png" width="2" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-27969.png" width="2" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-8974.png" width="61" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-28972.png" width="145" height="9" />                        

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-13172.png" width="73" height="9" />                                        600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-13609.png" width="23" height="21" />

 

                              600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-11025.png" width="121" height="38" />

 

图1.3.2 FIR滤波器的频率抽样型结构

 

    

 

1.4．快速卷积结构

 

根据圆周卷积的知识，我们知道将x(n)和h(n)都变成L点序列，即将600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-6706.png" width="22" height="23" />点输入x(n)补L-600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-21620.png" width="22" height="23" />个零值点，将600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-24620.png" width="23" height="23" />点冲激响应h(n)补L-600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-22839.png" width="23" height="23" />个零值点，只要满足：

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-30320.png" width="29" height="18" /> 600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-12009.png" width="22" height="23" />+600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-6523.png" width="23" height="23" />-1

 

则x(n)和h(n)的L点圆周卷积就代表它们的线性卷积。这样，我们就得到图1.4.1所示的快速卷积结构。

 

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-4224.png" width="86" height="33" />    x(n)                   X(k)

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-28470.png" width="86" height="33" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-4086.png" width="26" height="22" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7804.png" width="9" height="21" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-27207.png" width="37" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-963.png" width="73" height="9" />                                Y(k)

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-22506.png" width="109" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-29714.png" width="37" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-9844.png" width="9" height="32" />                                                   y(n)=x(n)*h(n)

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-18605.png" width="37" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-3091.png" width="50" height="33" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-286.png" width="37" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-27636.png" width="86" height="33" />

 

                           H(k)                                

 

                  图1.4.1 FIR滤波器的快速卷积结构

 

 

1.5．线性相位FIR滤波器结构

 

    当满足h(n)= 600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-30339.png" width="15" height="17" />h(N-1-n),0600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-15063.png" width="14" height="17" />n600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-12870.png" width="14" height="17" />N。FIR滤波器具有线性相位。

 

下面对N分为奇数和偶数两种情况分别加以讨论。

 

当N为奇数时，代入线性相位奇偶条件600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-28006.png" width="82" height="22" />=600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-19376.png" width="15" height="17" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-26112.png" width="34" height="22" />，可得

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-22627.png" width="311" height="58" />       （1.5.1）

 

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-28054.png" width="9" height="94" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-10360.png" width="9" height="125" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-22740.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-29541.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-29877.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-16874.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23114.png" width="25" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-30434.png" width="169" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-32485.png" width="9" height="125" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-24747.png" width="9" height="125" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-21597.png" width="9" height="73" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23276.png" width="49" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23614.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-11130.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-19868.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23398.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-10853.png" width="37" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-5501.png" width="85" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-18537.png" width="85" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7613.png" width="37" height="32" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-13163.png" width="25" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-20881.png" width="25" height="32" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-14589.png" width="25" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-24275.png" width="25" height="32" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-13298.png" width="25" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-4063.png" width="25" height="32" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7340.png" width="25" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-15676.png" width="49" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-19602.png" width="37" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-5738.png" width="25" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-29613.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-8827.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-8066.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-13455.png" width="85" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-29531.png" width="85" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-19802.png" width="61" height="9" />x(n)         600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-17367.png" width="23" height="21" />       600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-12446.png" width="23" height="21" />             600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-8322.png" width="23" height="21" />        600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-31069.png" width="23" height="21" /> 

 

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-21421.png" width="9" height="125" />         600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-15048.png" width="15" height="17" />1        600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-30020.png" width="15" height="17" />1       600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-16538.png" width="15" height="17" />1             600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-20393.png" width="15" height="17" />1

 

                                         

 

             600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-27380.png" width="23" height="21" />       600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-11422.png" width="23" height="21" />             600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-9771.png" width="23" height="21" />        600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-21079.png" width="23" height="21" /> 

 

        h(0)      h(1)       600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-31261.png" width="81" height="42" />     600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-2172.png" width="61" height="42" />          

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-5434.png" width="73" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-24865.png" width="85" height="2" />                                                            y(n)    

 

           图1.5.1 N为奇数时线性相位FIR滤波器的直接结构                                                   

 

 

当N为偶数时，代入线性相位奇偶条件600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-6652.png" width="34" height="22" />=600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-234.png" width="15" height="17" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-8720.png" width="82" height="22" />，可得

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23932.png" width="202" height="58" />                     （1.5.2）

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-11404.png" width="9" height="73" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-24976.png" width="25" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-10584.png" width="25" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-30009.png" width="25" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-24793.png" width="25" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-17757.png" width="25" height="42" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-8722.png" width="85" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-11237.png" width="37" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-12939.png" width="25" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-26218.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-5830.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-30583.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-16138.png" width="61" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-22631.png" width="61" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-6034.png" width="61" height="9" />   x(n)          600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-28224.png" width="23" height="21" />     600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-14035.png" width="23" height="21" />            600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7088.png" width="23" height="21" />         600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-1036.png" width="23" height="21" />

 

     

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-19987.png" width="9" height="136" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-20186.png" width="9" height="136" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-14177.png" width="9" height="136" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-26337.png" width="9" height="136" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-21641.png" width="9" height="136" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-12646.png" width="25" height="32" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7393.png" width="37" height="32" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-554.png" width="25" height="32" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-4438.png" width="25" height="32" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-17448.png" width="25" height="32" />           600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-29279.png" width="15" height="17" />1     600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7332.png" width="15" height="17" />1    600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-9293.png" width="15" height="17" />1              600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-19028.png" width="15" height="17" />1      600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-28644.png" width="15" height="17" />1

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-3128.png" width="73" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-21603.png" width="49" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-6110.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-24357.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-25371.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-23816.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-25669.png" width="61" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-7219.png" width="61" height="9" />

 

       600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-17768.png" width="23" height="21" />      600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-26875.png" width="23" height="21" />             600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-10776.png" width="23" height="21" />            600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-1778.png" width="23" height="21" />                                

 

     h(0)    h(1)   h(2) …          600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-25796.png" width="65" height="42" />  600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-12130.png" width="61" height="42" />

 

600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-8121.png" width="25" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-10444.png" width="157" height="9" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-24382.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-26394.png" width="25" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-11617.png" width="13" height="2" />600)makesmallpic(this,600,1800);' src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image-25254.png" width="133" height="2" />                                                        y(n)

 

          

 

图1.5.2 N为偶数时线性相位FIR滤波器的直接结构

 

                       

 

由以上流图看出线性相位FIR滤波器结构比一般直接型结构可以节省一半数量的乘法次数。

 

除了上述的各种结构，还有一种新的结构形式，即格型（Lattice）结构。事实证明：① 由于它的模块化结构便于实现高速并行处理；② 一个m阶格型滤波器可以产生从1阶到m阶的m个横向滤波器的输出性能；③ 它对有限长的舍入误差不灵敏。由于这些优点，此结构在现代谱估计、语音信号处理、自适应滤波等方面得到了广泛应用[4]。限于篇幅关系，这里就不做详细介绍了。

上一篇：MSP430单片机与液晶显示器的串行接口方案设计(一 下一篇：基于MFCC和神经阵列网络的声纹识别系统-通信工程