1、實驗四IIR 數字濾波器的設計一. 實驗目的(1掌握雙線性變換法及脈沖相應不變法設計IIR 數字濾波器的具體設計方法及其原理，熟悉用雙線性變換法及脈沖響應不變法設計低通、高通和帶通IIR 數字濾波器的計算機編程。(2觀察雙線性變換及脈沖響應不變法設計的濾波器的頻域特性，了解雙線性變換法及脈沖響應不變法的特點。(3熟悉巴特沃思濾波器、切比雪夫濾波器和橢圓濾波器的頻率特性。二. 實驗內容(1f c =0.3kHz，=0.8dB，f r =0.2kHz，At=20dB，T=1ms；設計一切比雪夫高通濾波器，觀察其通帶損耗和阻帶衰減是否滿足要求。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('切比雪夫模擬高通濾波器'

3、; 分析：(2f c =0.2kHz，=1dB，f r =0.3kHz，At=25dB，T=1ms；分別用脈沖響應不變法及雙線性變換法設計一巴特沃思數字低通濾波器，觀察所設計數字濾波器的幅頻特性曲線，記錄帶寬和衰減量，檢查是否滿足要求。比較這兩種方法的優缺點。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;%脈沖相應不變法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;%雙線性變換法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('巴特沃思數字低通濾波器'legend('脈沖相應不變法',' 雙線性變換法',1; 分析：(3利用雙線性變換法分別設計滿足下列指標的巴特沃思型、切比雪夫型和橢圓型數字低通濾波器，并作圖驗證設計結果:f c =1.2kHz，0.5dB，f r =2kHz,，At40dB，f s =8kHz。比較這三種濾波器的階數。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'%橢圓型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('三種數字低通濾波器'legend(&

8、#39;巴特沃思數字低通濾波器',' 切比雪夫數字低通濾波器',' 橢圓數字低通濾波器',3; 分析：(4分別用脈沖響應不變法和雙線性變換法設計一巴特沃思型數字帶通濾波器，已知f s =30kHz，其等效的模擬濾波器指標為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;%脈沖相應不變法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;%雙線性變換法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('巴特沃思數字帶通濾波器'legend('脈沖相應不變法',' 雙線性變換法',1; 分析：實現最小阻帶衰減不對稱：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('巴特沃思數字帶通濾波器' 分析

13、：(5 用利用雙線性變換法設計滿足下列指標的切比雪夫型數字帶阻濾波器，并作圖驗證設計 結果：當 1kHzf2kHz 時，At18dB；當 f 500Hz 以及 f 3kHz 時，3dB；采 樣頻率 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&