“免费”FIR数字滤波器的MATLAB实现(一).doc

“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” /                     （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” /              （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:/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” /                             （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:/docume1/admini1/locals1/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:/docume1/admini1/locals1/temp/ksohtml/wps_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” /                   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=“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); 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/locals1/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-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)makesmallpic(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=“file:/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/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” 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)makesmallpic(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:/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)    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:/docume1/admini1/locals1/temp/ksohtml/wps_clip_image-29973.png” width=“330” height=“58” /        （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_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/temp/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.png” 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)makesmallpic(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:/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/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” width=“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)makesmallpic(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:/docume1/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/ksohtml/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=“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(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:/docume1/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); 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-14969.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” /          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/locals1/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,600,1800); 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” /     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_clip_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:/docume1/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” /         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” /            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h(z)的内插公式为 600)makesmallpic(this,600,1800); src=“file:/c:/docume1/admini1/locals1/temp/ksohtml/wps_clip_image-2168.png” width=“13” height=“23” /      600)makesmallpic(this,600,1800); src=“file:/c:/docume1/admini1/locals1/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:/docume1/admini1/locals1/temp/ksohtml/wps_clip_image-32081.png” width=“45” height=“25” /=600)makesmallpic(this,600,1800); src=“file:/c:/docume1/admini1/locals1/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:/docume1/admini1/locals1/temp/ksohtml/wps_clip_image-7224.png” width=“45” height=“25” /=600)makesmallpic(this,600,1800); src=“file:/c:/docume1/admini1/locals1/temp/ksohtml/wps_clip_image-24869.png” width=“49” height=“21” /=0 则有 600)makesmallpic(this,600,1800); src=“file:/c:/docume1/admini1/locals1/temp/ksohtml/wps_clip_image-29295.png” width=“90” height=“26” / 600)makesmallpic(this,600,1800); src=“file:/c:/docume1/admini1/locals1/temp/ksohtml/wps_clip_image-10127.png” width=“65” height=“38” /，  600)makesmallpic(this,600,1800); src=“file:/c:/docume1/admini1/locals1/temp/ksohtml/wps_clip_image-29092.png” width=“23” height=“18” /0，1，,n-1 即600)makesmallpic(this,600,1800); src=“file:/c:/docume1/admini1/locals1/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:/docume1/admini1/locals1/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:/docume1/admini1/locals1/temp/ksohtml/wps_clip_image-18800.png” width=“163” height=“46” / 相角为  600)makesmallpic(this,600,1800); src=“file:/c:/docume1/admini1/locals1/temp/ksohtml/wps_clip_image-31818.png” width=“37” height=“137” /                              600)makesmallpic(this,600,1800); src=“file:/c:/docume1/admini1/locals1/temp/ksohtml/wps_clip_image-6702.png” width=“