实验11用MATLAB设计FIR数字滤波器综述

1、课程名称：数字信号处理实验报告院系:班级:学号:姓名:信息工程学院电信二班实验成绩:指导教师:日期:第11页共9页实验11用MATLAB设计FIR数字滤波器、实验目的:1、 加深对窗函数法设计FIR数字滤波器的基本原理的理解。2、 学习用MATLAB语言的窗函数法编写设计FIR数字滤波器的程序。3、 了解MATLAB语言有关窗函数法设计FIR数字滤波器的常用函数用法。二、实验内容及步骤2、选择合适的窗函数设计FIR数字低通滤波器，要求：Wp=0.2 n,Rp=0.05dB ; Ws=0.3 n,As=40dB。描绘该滤波器的脉冲响应、窗函数及滤波器的幅频响应曲线和相频响应曲线。分析：根据设计指

2、标要求，并查表 11-1，选择汉宁窗。程序清单如下：function hd=ideal_lp(wc,N)wp=0.2*pi;ws=0.3*pi;deltaw=ws-wp;tao=(N-1)/2;n=0:(N-1);m=n-tao+eps; hd=sin(wc*m)./(pi*m);function db,mag,pha,grd,w=freqz_m(b,a);H,w=freqz(b,a,1000,whole);H=(H(1:501);w=(w(1:501);mag=abs(H);db=20*log10(mag+eps)/max(mag);pha=a ngle(H);grd=grpdelay(b,

3、a,w);wp=0.2*pi;ws=0.3*pi;deltaw=ws-wp;wc=(ws+wp)/2;N0=ceil(6.6*pi/deltaw);N=N0+mod(N0+1,2)win dows=(ha nnin g(N);hd=ideal_lp(wc,N);b=hd.*w in dows;db,mag,pha,grd,w=freqz_m(b,1);n=0:N-1;dw=2*pi/1000;Rp=-(min(db(1:wp/dw+1) % 检验通带波动As=-round(max(db(ws/dw+1:501) % 检验最小阻带衰减 subplot(2,2,1);stem( n,b);axis

4、(0,N,1.1*min(b),1.1*max(b);title(实际脉冲响应);xlabel( n);ylabel(h( n);subplot(2,2,2);stem (n,win dows);axis(O,N,O,1.1);title(窗函数特性);xlabel( n);ylabel(wd( n);subplot(2,2,3);plot(w/pi,db);axis(0,1,-80,10);title(幅度频率响应);xlabel(频率(单位：pi) );ylabel(H(eAjomega); set(gca,XTickMode,ma nual,XTick,0,wp/pi,ws/pi,1);

5、 set(gca,YTickMode,ma nual,YTick,-50,-20,-3,0);grid subplot(2,2,4);plot(w/pi,pha);axis(O,1,-4,4);title(相位频率响应);xlabel(频率(单位：pi) );ylabel(phi(omega);set(gca,XTickMode,ma nual,XTick,0,wp/pi,ws/pi,1);set(gca,YTickMode,ma nual,YTick,-3.1416,0,3.1416,4);gridN =67Rp =0.0706As = 44实际脉冲响应-0-20-5000.20.3频率（单

6、位：-）1|幅度频率响应窗函数特性n相位频率响应3、用凯塞窗设计一个 FIR数字高通滤波器，要求：wp=0.3 n, Rp=0.1dB ; ws=0.2 n,As=50dB。描绘该滤波器的脉冲响应、窗函数及滤波器的幅频响应曲线和相频响应曲线程序清单如下：function hd=ideal_lp(wc,N)tao=(N-1)/2;n=0:(N-1);m=n-tao+eps;hd=sin(wc*m)./(pi*m);function db,mag,pha,grd,w=freqz_m(b,a);H,w=freqz(b,a,1000,whole);H=(H(1:501);w=(w(1:501);mag

7、=abs(H);db=20*log10(mag+eps)/max(mag);pha=a ngle(H);grd=grpdelay(b,a,w);wp=0.3*pi;ws=0.2*pi;deltaw=wp-ws;N0=ceil(6.6*pi/deltaw);N=N0+mod(N0+1,2)wi ndows=(kaiser(N,7.865);wc=(ws+wp)/2;hd=ideal_lp(pi,N)-ideal_lp(wc,N);b=hd.*w in dows;db,mag,pha,grd,w=freqz_m(b,1);n=0:N-1;dw=2*pi/1000;Rp=-(min(db(wp/dw

8、+1:501) % 检验通带波动As=-round(max(db(1:ws/dw+1) % 检验最小阻带衰减 subplot(2,2,1);stem( n,b);axis(0,N,1.1*min(b),1.1*max(b);title(实际脉冲响应);xlabel( n);ylabel(h( n);subplot(2,2,2);stem (n,win dows);axis(O,N,O,1.1);title(窗函数特性);xlabel( n);ylabel(wd( n);subplot(2,2,3);plot(w/pi,db);axis(0,1,-100,2);title(幅度频率响应);xla

9、bel(频率(单位：pi) );ylabel(H(eAjomega); set(gca,XTickMode,ma nual,XTick,0,ws/pi,wp/pi,1); set(gca,YTickMode,ma nual,YTick,-40-20,-3,0);grid subplot(2,2,4);plot(w/pi,pha);axis(0,1,-4,4);title(相位频率响应);xlabel(频率(单位：pi) );ylabel(phi(omega);set(gca,XTickMode,ma nual,XTick,0,ws/pi,wp/pi,1);set(gca,YTickMode,m

10、a nual,YTick,-pi,O,pi);gridN =67Rp = 0.2321As =32-3窗函数特性0.500.20.3频率（单位：-）-600 .一.0204060n相位频率响应4、选择合适的窗函数设计一个FIR数字带通滤波器，要求：fpi=3.5kHz , fp2=6.5kHz ,Rp=0.05dB ； fs1=2.5kHz，fs2=7.5kHz，As=60dB。滤波器采样频率 Fs=20kHz。描绘该滤波器 的脉冲响应、窗函数及滤波器的幅频响应曲线和相频响应曲线。分析：根据设计指标应选择布莱克曼窗。程序清单如下：function db,mag,pha,grd,w=freqz_

11、m(b,a);H,w=freqz(b,a,1000,whole);H=(H(1:501);w=(w(1:501);mag=abs(H);db=20*log10(mag+eps)/max(mag);pha=a ngle(H);grd=grpdelay(b,a,w);fp1=3.5;fp2=6.5;fs1=2.5;fs2=7.5;Fs=20;ws1=fs1/(Fs/2)*pi;ws2=fs2/(Fs/2)*pi;wp仁fp1/(Fs/2)*pi;wp2=fp2/(Fs/2)*pi;deltaw=wp1-ws1;N0=ceil(11*pi/deltaw);N=N0+mod(N0+1,2) %为实现F

12、IR类型1偶对称滤波器，应确保N为奇数wi ndows=blackma n( N);wc1=(ws1+wp1)/2/pi;wc2=(ws2+wp2)/2/pi;b=fir1(N-1,wc1,wc2,wi ndows);db,mag,pha,grd,w=freqz_m(b,1);n=0:N-1;dw=2*pi/1000;Rp=-(mi n( db(wp1/dw+1:wp2/dw+1) % 检验通带波动ws0=1:ws1/dw+1,ws2/dw+1:501;% 建立阻带频率样点数组As=-round(max(db(wsO) %检验最小阻带衰减subplot(2,2,1);stem( n,b);ax

13、is(0,N,1.1*min(b),1.1*max(b);title(实际脉冲响应);xlabel( n);ylabel(h( n);subplot(2,2,2);stem (n,win dows);axis(O,N,O,1.1);title(窗函数特性);xlabel( n);ylabel(wd( n);subplot(2,2,3);plot(w/pi,db);axis(0,1,-150,10);title(幅度频率响应);xlabel(频率(单位：pi) );ylabel(H(eAjomega);set(gca,XTickMode,ma nual,XTick,0,fs1,fp1,fp2,f

14、s2,500);set(gca,YTickMode,ma nual,YTick,-150,-40,-3,0);gridsubplot(2,2,4);plot(w/pi,pha);axis(0,1,-4,4);title(相位频率响应);xlabel(频率(单位：pi) );ylabel(phi(omega);set(gca,XTickMode,ma nual,XTick,0,fs1,fp1,fp2,fs2,500);set(gca,YTickMode,ma nual,YTick,-pi,O,pi);gridN =111Rp =0.0034As =740.4，0.2-t 0-Lar- 1 J 1

15、Llfefitaif.=-. J日丰-0.2实际脉冲响应050100n窗函数特性n相位频率响应幅度频率响应频率(单位：二)频率(单位：)5、选择合适的窗函数设计一个FIR数字带阻滤波器，要求：fpi=1kHz, fp2=4.5kHz ,R=0.1dB ； fsi=2kHz，f s2=3.5kHz，A=40dB。滤波器采样频率 Fs=10kHz。描绘该滤波器的脉 冲响应、窗函数及滤波器的幅频响应曲线和相频响应曲线。分析：根据设计指标选择汉宁窗。程序清单如下：function hd=ideal_lp(wc,N)tao=(N-1)/2;n=0:(N-1);m=n-tao+eps;hd=sin(wc*

16、m)./(pi*m);function db,mag,pha,grd,w=freqz_m(b,a);H,w=freqz(b,a,1000,whole);H=(H(1:501);w=(w(1:501);mag=abs(H);db=20*log10(mag+eps)/max(mag);pha=a ngle(H);grd=grpdelay(b,a,w);fp仁 1;fp2=4.5;fs1=2;fs2=3.5;Fs=10;ws仁fs1/(Fs/2)*pi;ws2=fs2/(Fs/2)*pi;wp仁fp1/(Fs/2)*pi;wp2=fp2/(Fs/2)*pi;wp=wp1,wp2;ws=ws1,ws2

17、;deltaw=ws1-wp1;N0=ceil(6.2*pi/deltaw);N=N0+mod(N0+1,2) %为实现FIR类型1偶对称滤波器，应确保N为奇数win dows=(ha nnin g(N);wc1=(ws1+wp1)/2;wc2=(ws2+wp2)/2;hd=ideal_lp(wc1,N)+ideal_lp(pi,N)-ideal_lp(wc2,N);% 建立理想带阻 b=hd.*w in dows;db,mag,pha,grd,w=freqz_m(b,1);n=0:N-1;dw=2*pi/1000;wp0=1:wp1/dw+1,wp2/dw+1:501;% 建立通带频率样点数

18、组As=-rou nd(max(db(ws1/dw+1:ws2/dw+1) % 检验最小阻带衰减Rp=-(min(db(wpO) % 检验通带波动subplot(2,2,1);stem( n,b);axis(0,N,1.1*min(b),1.1*max(b);title( 实际脉冲响应);xlabel( n);ylabel(h( n);subplot(2,2,2);stem (n,win dows);axis(O,N,O,1.1);title(窗函数特性);xlabel( n);ylabel(wd( n);subplot(2,2,3);plot(w/pi,db);axis(0,1,-150,10);title(幅度频率响应);xlabel(频率(单位：pi) );ylabel(H(eAjomega);set(gca,XTickMode,ma nual,XTick,0,wp1/pi,ws1/pi,ws2/pi,wp2/pi,1);set(gca,YTickMode,ma nual,YTick,-150,-40,-3,0);gridsubplot(2,2,4);plot(w/pi,pha);axis(0,1,-4,4);title(相位频率响应);xlabel(频率(单位：pi) );ylabel(phi(om