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1、“免费”FIR数字滤波器的MATLAB实现(一) FIR数字滤波器的MATLAB实现 1FIR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:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-22618.png” width=“198” height=“89” / &n
2、bsp; （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:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-28576.png” width=“254” height=“46” / &
3、nbsp; （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
4、序列，600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/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:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-16086.png” width=“133” height=“46” /
5、; （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
6、式为 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-31365.png” width=“173” height=“46” / &
7、nbsp; （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:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wp
8、s_clip_image-18097.png” width=“23” height=“21” / 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-7537.png” width=“23” height=“21” /
9、; 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-31896.png” width=“23” height=“21” / 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-13667.png” width=“97” height=“
10、9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-18161.png” width=“9” height=“63” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-25190.png” width=“61” height=“9” /600)makesmallpic(this,600,1800
11、); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-21465.png” width=“61” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-22395.png” width=“9” height=“63” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/L
12、OCALS1/Temp/ksohtml/wps_clip_image-6743.png” width=“9” height=“63” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-10089.png” width=“9” height=“63” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-
13、8480.png” width=“9” height=“63” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-21114.png” width=“13” height=“2” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-9.png” width=“13” height=“2” /600)m
14、akesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-13499.png” width=“25” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-6134.png” width=“25” height=“9” /600)makesmallpic(this,600,1800); src=“fi
15、le:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-8604.png” width=“13” height=“2” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-26313.png” width=“13” height=“2” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp
16、/ksohtml/wps_clip_image-13234.png” width=“13” height=“2” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-12890.png” width=“13” height=“2” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-5673.png”
17、width=“13” height=“2” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-23449.png” width=“13” height=“2” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-18465.png” width=“61” height=“9” /600)makesma
18、llpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-23983.png” width=“61” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-5765.png” width=“61” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:
19、/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-7864.png” width=“61” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-20588.png” width=“61” height=“9” / h(0)
20、;h(1) h(2) h(N-2) h(N-1) &nb
21、sp; y(n)
22、; 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:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-29973.png” width=“330” height=“58” /
23、 （1.2.1） 其中600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/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:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip
24、_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:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-32666.png” width=“9” height=“53” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/T
25、emp/ksohtml/wps_clip_image-21255.png” width=“9” height=“63” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-6065.png” width=“97” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-23054.pn
26、g” width=“97” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-14934.png” width=“9” height=“53” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-23060.png” width=“9” height=“63” /600)make
27、smallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-21769.png” width=“9” height=“63” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-16848.png” width=“9” height=“53” /600)makesmallpic(this,600,1800); src=“file
28、:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-24051.png” width=“85” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-22621.png” width=“85” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/
29、ksohtml/wps_clip_image-7400.png” width=“9” height=“53” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-7381.png” width=“9” height=“63” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-8912.png” wid
30、th=“13” height=“2” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-22024.png” width=“85” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-10649.png” width=“13” height=“2” /600)makesmallp
31、ic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-28968.png” width=“13” height=“2” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-30179.png” width=“13” height=“2” /600)makesmallpic(this,600,1800); src=“file:/C:/D
32、OCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-12013.png” width=“85” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-25042.png” width=“85” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtm
33、l/wps_clip_image-21509.png” width=“9” height=“53” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-11766.png” width=“9” height=“63” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-23290.png” width=
34、“73” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-32282.png” width=“73” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-17960.png” width=“9” height=“53” /600)makesmallpic(
35、this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-2530.png” width=“9” height=“63” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-6771.png” width=“73” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME
36、1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-1840.png” width=“73” height=“9” /600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-4255.png” width=“73” height=“9” / x(n) 600)makesmallpic(this,600,1800)
37、; src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-17550.png” width=“25” height=“25” / 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-14
38、969.png” width=“26” height=“25” / 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-23619.png” width=“37” height=“38” / &
39、nbsp; y(n) 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-560.png” width=“23” height=“21” / 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS
40、1/Temp/ksohtml/wps_clip_image-27837.png” width=“25” height=“23” / 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-23949.png” width=“23” height=“21” / 600)makesmallpic(this,600,180
41、0); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-26981.png” width=“25” height=“23” / 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-7157.png” width=“23” height=“21” /&n
42、bsp; 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-28458.png” width=“35” height=“38” / 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_cl
43、ip_image-11600.png” width=“23” height=“21” / 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-8766.png” width=“25” height=“23” / 600)makesmallpic(this,600,1800); src=“file:/C:/DOCU
44、ME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-29001.png” width=“23” height=“21” / 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-1751.png” width=“26” height=“23” /
45、600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-22924.png” width=“23” height=“21” / 600)makesmallpic(this,600,1800); src=“file:/C:/DOCUME1/ADMINI1/LOCALS1/Temp/ksohtml/wps_clip_image-5373.png” width=“38” height=“38
46、” / 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:/DOCUME1/ADMINI1/LOCALS1/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:/DOCUME1/ADMINI1/LOCALS1/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
