实验四 IIR数字滤波器的设计

1、实验四IIR 数字滤波器的设计一. 实验目的(1掌握双线性变换法及脉冲相应不变法设计IIR 数字滤波器的具体设计方法及其原理，熟悉用双线性变换法及脉冲响应不变法设计低通、高通和带通IIR 数字滤波器的计算机编程。(2观察双线性变换及脉冲响应不变法设计的滤波器的频域特性，了解双线性变换法及脉冲响应不变法的特点。(3熟悉巴特沃思滤波器、切比雪夫滤波器和椭圆滤波器的频率特性。二. 实验内容(1f c =0.3kHz，=0.8dB，f r =0.2kHz，At=20dB，T=1ms；设计一切比雪夫高通滤波器，观察其通带损耗和阻带衰减是否满足要求。clear all;wc=2*pi*300;wr=2*p

2、i*200;rp=0.8;rs=20;N,wn=cheb1ord(wc,wr,rp,rs,'s'num,den=cheby1(N,rp,wn,'high','s'omega =0:200:2000*pi;h =freqs(num,den,omega;gain =20*log10(abs(h;plot (omega/(2*pi,gain;axis(0,800,-80,10;grid;xlabel('Frequencyin Hz' ylabel('Gainin dB'title('切比雪夫模拟高通滤波器'

3、; 分析：(2f c =0.2kHz，=1dB，f r =0.3kHz，At=25dB，T=1ms；分别用脉冲响应不变法及双线性变换法设计一巴特沃思数字低通滤波器，观察所设计数字滤波器的幅频特性曲线，记录带宽和衰减量，检查是否满足要求。比较这两种方法的优缺点。clear all;wc=2*pi*200;wr=2*pi*300;rp=1;rs=25;fs=1000;N,wn=buttord(wc,wr,rp,rs,'s'B,A=butter(N,wn,'s'num1,den1=impinvar(B,A,fs;%脉冲相应不变法h1,w=freqz(num1,den1

4、;w1=2*fs*tan(wc/(2*fs;w2=2*fs*tan(wr/(2*fs;N,wn=buttord(w1,w2,rp,rs,'s'B,A=butter(N,wn,'s'num2,den2=bilinear(B,A,fs;%双线性变换法h2,w=freqz(num2,den2;f=w/pi*500;plot(f,20*log10(abs(h1,'-.',f,20*log10(abs(h2,'-'axis(0,500,-80,10;grid;xlabel('Frequencyin Hz' ylabel(&#

5、39;Gainin dB'title('巴特沃思数字低通滤波器'legend('脉冲相应不变法',' 双线性变换法',1; 分析：(3利用双线性变换法分别设计满足下列指标的巴特沃思型、切比雪夫型和椭圆型数字低通滤波器，并作图验证设计结果:f c =1.2kHz，0.5dB，f r =2kHz,，At40dB，f s =8kHz。比较这三种滤波器的阶数。clear all;wc=2*pi*1200;wr=2*pi*2000;rp=0.5;rs=40;fs=8000;w1=2*fs*tan(wc/(2*fs;w2=2*fs*tan(wr/(2

6、*fs;Nb,wn=buttord(w1,w2,rp,rs,'s'%巴特沃思B,A=butter(Nb,wn,'s'num1,den1=bilinear(B,A,fs;h1,w=freqz(num1,den1;Nc,wn=cheb1ord(w1,w2,rp,rs,'s'%切比雪夫B,A=cheby1(Nc,rp,wn,'s'num2,den2=bilinear(B,A,fs;h2,w=freqz(num2,den2;Ne,wn=ellipord(w1,w2,rp,rs,'s'%椭圆型B,A=ellip(Ne,rp,

7、rs,wn,'low','s'num3,den3=bilinear(B,A,fs;h3,w=freqz(num3,den3;f=w/pi*4000;plot(f,20*log10(abs(h1,'-',f,20*log10(abs(h2,'-',f,20*log10(abs(h3,':'axis(0,3000,-100,10;grid;xlabel('Frequencyin Hz' ylabel('Gainin dB'title('三种数字低通滤波器'legend(&

8、#39;巴特沃思数字低通滤波器',' 切比雪夫数字低通滤波器',' 椭圆数字低通滤波器',3; 分析：(4分别用脉冲响应不变法和双线性变换法设计一巴特沃思型数字带通滤波器，已知f s =30kHz，其等效的模拟滤波器指标为3dB ，2kHz f 3kHz ；At 5dB, f 6kHz ；At 20dB ，f 1.5kHz 。clear all;wc=2*pi*20002*pi*3000;wr=2*pi*15002*pi*6000;rp=3;rs=20;fs=30000;N,wn=buttord(wc,wr,rp,rs,'s'B,A=bu

9、tter(N,wn,'s'num1,den1=impinvar(B,A,fs;%脉冲相应不变法h1,w=freqz(num1,den1;w1=2*fs*tan(2*pi*2000/(2*fs;w2=2*fs*tan(2*pi*3000/(2*fs;wr1=2*fs*tan(2*pi*1500/(2*fs;wr2=2*fs*tan(2*pi*6000/(2*fs;N,wn=buttord(w1,w2,wr1,wr2,rp,rs,'s'B,A=butter(N,wn,'s'num2,den2=bilinear(B,A,fs;%双线性变换法h2,w=f

10、reqz(num2,den2;f=w/pi*15000;plot(f,20*log10(abs(h1,'-.',f,20*log10(abs(h2,'-'axis(500,7000,-30,10;grid;xlabel('Frequencyin Hz' ylabel('Gainin dB'title('巴特沃思数字带通滤波器'legend('脉冲相应不变法',' 双线性变换法',1; 分析：实现最小阻带衰减不对称：clear all;wc=2*pi*3000;wr=2*pi*6000

11、;rp=3;rs=5;fs=30000;w1=2*fs*tan(wc/(2*fs;w2=2*fs*tan(wr/(2*fs;N,wn=buttord(w1,w2,rp,rs,'s'%巴特沃思低通B,A=butter(N,wn,'s'num1,den1=bilinear(B,A,fs;h1,w=freqz(num1,den1;wc=2*pi*2000;wr=2*pi*1500;rp=3;rs=20;fs=30000;w1=2*fs*tan(wc/(2*fs;w2=2*fs*tan(wr/(2*fs;N,wn=buttord(w1,w2,rp,rs,'s&#

12、39;%巴特沃思高通B,A=butter(N,wn,'high','s'num2,den2=bilinear(B,A,fs;h2,w=freqz(num2,den2;f=w/pi*15000;g1=20*log10(abs(h1;g2=20*log10(abs(h2;g=vertcat(g2(1:76,g1(77:512;plot(f,g;axis(0,6500,-30,10;grid;xlabel('Frequencyin Hz' ylabel('Gainin dB' title('巴特沃思数字带通滤波器' 分析

13、：(5 用利用双线性变换法设计满足下列指标的切比雪夫型数字带阻滤波器，并作图验证设计 结果：当 1kHzf2kHz 时，At18dB；当 f 500Hz 以及 f 3kHz 时，3dB；采 样频率 f s =10kHz。 clear all; rp=3;rs=18;fs=10000; wr1=2*fs*tan(2*pi*1000/(2*fs; wr2=2*fs*tan(2*pi*2000/(2*fs; w1=2*fs*tan(2*pi*500/(2*fs; w2=2*fs*tan(2*pi*3000/(2*fs; N,wn=cheb1ord(w1 w2,wr1 wr2,rp,rs,'s' B,A=cheby1(N,rp,wn,'stop','s' num,den=bilinear(B,A,fs; h,w=freqz(num,den; f=w/pi*5000; plot(f,20*log10(abs(h; axis(100,3500,-30,10;grid; xlabel('Frequency in Hz&