實驗四 IIR數(shù)字濾波器的設(shè)計

1、實驗四IIR 數(shù)字濾波器的設(shè)計一. 實驗目的(1掌握雙線性變換法及脈沖相應不變法設(shè)計IIR 數(shù)字濾波器的具體設(shè)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(shè)計低通、高通和帶通IIR 數(shù)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(shè)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(nèi)容(1f c =0.3kHz，=0.8dB，f r =0.2kHz，At=20dB，T=1ms；設(shè)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(shè)計一巴特沃思數(shù)字低通濾波器，觀察所設(shè)計數(shù)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(yōu)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(shù)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(shè)計滿足下列指標的巴特沃思型、切比雪夫型和橢圓型數(shù)字低通濾波器，并作圖驗證設(shè)計結(jié)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(shù)。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(shù)字低通濾波器'legend(&

8、#39;巴特沃思數(shù)字低通濾波器',' 切比雪夫數(shù)字低通濾波器',' 橢圓數(shù)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(shè)計一巴特沃思型數(shù)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(shù)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(xiàn)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(shù)字帶通濾波器' 分析

13、：(5 用利用雙線性變換法設(shè)計滿足下列指標的切比雪夫型數(shù)字帶阻濾波器，并作圖驗證設(shè)計 結(jié)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&