第頁(yè)課程名稱：課程名稱：數(shù)字信號(hào)處理實(shí)驗(yàn)報(bào)告院系：信息工程學(xué)院實(shí)驗(yàn)7用MATLAB設(shè)計(jì)IIR數(shù)字濾波器一、實(shí)驗(yàn)?zāi)康模?、加深對(duì)IIR數(shù)字濾波器的基本設(shè)計(jì)方法的理解。2、掌握用模擬濾波器原型設(shè)計(jì)IIR數(shù)字濾波器的方法。3、了解MATLAB有關(guān)IIR數(shù)字濾波器設(shè)計(jì)的子函數(shù)的調(diào)用方法。二、實(shí)驗(yàn)內(nèi)容及步驟1、閱讀并輸入實(shí)驗(yàn)原理中介紹的例題程序，觀察輸出的數(shù)據(jù)和圖形，結(jié)合基本原理理解每一條語(yǔ)句的含義。2、用雙線性變換法設(shè)計(jì)切比雪夫Ⅱ型數(shù)字濾波器，列出傳遞函數(shù)并描繪模擬和數(shù)字濾波器的幅頻響應(yīng)曲線。①設(shè)計(jì)一個(gè)數(shù)字低通濾波器，要求：ωp=0.2П，Rp=1dB；阻帶：ωs=0.35П，As=15dB，濾波器采樣頻率Fs=10Hz。wp=0.2*pi;%濾波器的通帶截止頻率ws=0.35*pi;%濾波器的阻帶截止頻率Rp=1;As=15;%濾波器的通阻帶衰減指標(biāo)ripple=10^(-Rp/20);%濾波器的通帶衰減對(duì)應(yīng)的幅度值A(chǔ)ttn=10^(-As/20);%濾波器的阻帶衰減對(duì)應(yīng)的幅度值%轉(zhuǎn)換為模擬濾波器的技術(shù)指標(biāo)Fs=10;T=1/Fs;Omgp=(2/T)*tan(wp/2);%原型通帶頻率的預(yù)修正Omgs=(2/T)*tan(ws/2);%原型阻帶頻率的預(yù)修正%模擬原型濾波器計(jì)算[n,Omgc]=buttord(Omgp,Omgs,Rp,As,'s')%計(jì)算階數(shù)n和截止頻率[z0,p0,k0]=buttap(n);%設(shè)計(jì)歸一化的巴特沃思模擬濾波器原型ba1=k0*real(poly(z0));%求原型濾波器的系數(shù)baa1=real(poly(p0));%求原型濾波器的系數(shù)a[ba,aa]=lp2lp(ba1,aa1,Omgc);%變換為模擬低通濾波器%也可將以上4行替換為[bb,aa]=butter(n,Omgc,'s');直接求模擬濾波器系數(shù)%用雙線性變換法計(jì)算數(shù)字濾波器系數(shù)[bd,ad]=bilinear(ba,aa,Fs)[sos,g]=tf2sos(bd,ad)%轉(zhuǎn)換成級(jí)聯(lián)型%求數(shù)字系統(tǒng)的頻率特性[H,w]=freqz(bd,ad);dbH=20*log10((abs(H)+eps)/max(abs(H)));subplot(2,2,1);plot(w/pi,abs(H));ylabel('|H|');title('幅度響應(yīng)');axis([0,1,0,1.1]);set(gca,'XTickMode','manual','XTick',[0,0.25,0.4,1]);set(gca,'YTickMode','manual','YTick',[0,Attn,ripple,1]);gridsubplot(2,2,2);plot(w/pi,angle(H)/pi);ylabel('\phi');title('相位響應(yīng)');axis([0,1,-1,1]);set(gca,'XTickMode','manual','XTick',[0,0.25,0.4,1]);set(gca,'YTickMode','manual','YTick',[-1,0,1]);gridsubplot(2,2,3);plot(w/pi,dbH);title('幅度響應(yīng)(dB)');ylabel('dB');xlabel('頻率(\pi)');axis([0,1,-40,5]);set(gca,'XTickMode','manual','XTick',[0,0.25,0.4,1]);set(gca,'YTickMode','manual','YTick',[-50,-15,-1,0]);gridsubplot(2,2,4);zplane(bd,ad);axis([-1.1,1.1,-1.1,1.1]);title('零極點(diǎn)圖');②設(shè)計(jì)一個(gè)數(shù)字高通濾波器，要求：ωp=0.35П，Rp=1dB；阻帶：ωs=0.2П，As=15dB，濾波器采樣頻率Fs=10Hz。fs=1;fp=1.75;Fs=10;T=1/Fs;wp=fp/Fs*2*pi;%濾波器的通帶截止頻率ws=fs/Fs*2*pi;%濾波器的阻帶截止頻率Rp=1;As=15;%濾波器的通阻帶衰減指標(biāo)ripple=10^(-Rp/20);%濾波器的通帶衰減對(duì)應(yīng)的幅度值A(chǔ)ttn=10^(-As/20);%濾波器的阻帶衰減對(duì)應(yīng)的幅度值%轉(zhuǎn)換為模擬濾波器的技術(shù)指標(biāo)Omgp=(2/T)*tan(wp/2);%原型通帶頻率的預(yù)修正Omgs=(2/T)*tan(ws/2);%原型阻帶頻率的預(yù)修正%模擬原型濾波器計(jì)算[n,Omgc]=ellipord(Omgp,Omgs,Rp,As,'s')%計(jì)算階數(shù)n和截止頻率[z0,p0,k0]=ellipap(n,Rp,As);%設(shè)計(jì)歸一化的橢圓濾波器原型ba1=k0*real(poly(z0));%求原型濾波器的系數(shù)baa1=real(poly(p0));%求原型濾波器的系數(shù)a[ba,aa]=lp2hp(ba1,aa1,Omgc);%變換為模擬高通濾波器%用雙線性變換法計(jì)算數(shù)字濾波器系數(shù)[bd,ad]=bilinear(ba,aa,Fs)%求數(shù)字系統(tǒng)的頻率特性[H,w]=freqz(bd,ad);dbH=20*log10((abs(H)+eps)/max(abs(H)));subplot(2,2,1);plot(w/2/pi*Fs,abs(H),'k');ylabel('|H|');title('幅度響應(yīng)');axis([0,Fs/2,0,1.1]);set(gca,'XTickMode','manual','XTick',[0,fs,fp,Fs/2]);set(gca,'YTickMode','manual','YTick',[0,Attn,ripple,1]);gridsubplot(2,2,2);plot(w/2/pi*Fs,angle(H)/pi*180,'k');ylabel('\phi');title('相位響應(yīng)');axis([0,Fs/2,-180,180]);set(gca,'XTickMode','manual','XTick',[0,fs,fp,Fs/2]);set(gca,'YTickMode','manual','YTick',[-180,0,180]);gridsubplot(2,2,3);plot(w/2/pi*Fs,dbH);title('幅度響應(yīng)(dB)');ylabel('dB');xlabel('頻率(\pi)');axis([0,Fs/2,-40,5]);set(gca,'XTickMode','manual','XTick',[0,fs,fp,Fs/2]);set(gca,'YTickMode','manual','YTick',[-50,-20,-1,0]);gridsubplot(2,2,4);zplane(bd,ad);axis([-1.1,1.1,-1.1,1.1]);title('零極點(diǎn)圖');n=2Omgc=12.2560bd=0.5214-0.91870.5214ad=1.0000-0.75160.44923、設(shè)計(jì)一個(gè)切比雪夫Ⅱ型數(shù)字帶通濾波器，要求：；阻帶，濾波器采樣周期Ts=0.001s。列出傳遞函數(shù)并作頻率響應(yīng)曲線和零極點(diǎn)分布圖。wp1=0.4*pi;wp2=0.6*pi;%濾波器的通帶截止頻率ws1=0.3*pi;ws2=0.7*pi;%濾波器的阻帶截止頻率Rp=1;As=20;%濾波器的通阻帶衰減指標(biāo)%轉(zhuǎn)換為模擬濾波器的技術(shù)指標(biāo)T=0.001;Fs=1/T;Omgp1=(2/T)*tan(wp1/2);Omgp2=(2/T)*tan(wp2/2);Omgp=[Omgp1,Omgp2];Omgs1=(2/T)*tan(ws1/2);Omgs2=(2/T)*tan(ws2/2);Omgs=[Omgs1,Omgs2];bw=Omgp2-Omgp1;w0=sqrt(Omgp1*Omgp2);%模擬通帶帶寬和中心頻率%bw=Omgs2-Omgs1;w0=sqrt(Omgs1*Omgs2);設(shè)計(jì)cheb2時(shí)用模擬阻帶帶寬和中心頻率ripple=10^(-Rp/20);%濾波器的通帶衰減對(duì)應(yīng)的幅度值A(chǔ)ttn=10^(-As/20);%濾波器的阻帶衰減對(duì)應(yīng)的幅度值%模擬原型濾波器計(jì)算[n,Omgn]=cheb1ord(Omgp,Omgs,Rp,As,'s')%計(jì)算階數(shù)n和截止頻率[z0,p0,k0]=cheb1ap(n,Rp);%設(shè)計(jì)歸一化的模擬濾波器原型%[n,Omgn]=cheb2ord(Omgp,Omgs,Rp,As,'s')%[z0,p0,k0]=cheb2ap(n,As);%設(shè)計(jì)歸一化的cheb2型模擬濾波器原型ba1=k0*real(poly(z0));%求原型濾波器的系數(shù)baa1=real(poly(p0));%求原型濾波器的系數(shù)a[ba,aa]=lp2bp(ba1,aa1,w0,bw);%變換為模擬帶通濾波器%用雙線性變換法計(jì)算數(shù)字濾波器系數(shù)[bd,ad]=bilinear(ba,aa,Fs)%求數(shù)字系統(tǒng)的頻率特性[H,w]=freqz(bd,ad);dbH=20*log10((abs(H)+eps)/max(abs(H)));subplot(2,2,1);plot(w/pi,abs(H));ylabel('|H|');title('幅度響應(yīng)');axis([0,1,0,1.1]);set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,0.7,0.8]);set(gca,'YTickMode','manual','YTick',[0,Attn,ripple,1]);gridsubplot(2,2,2);plot(w/pi,angle(H)/pi*180);ylabel('\phi');title('相位響應(yīng)');axis([0,1,-180,180]);set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,0.7,0.8]);set(gca,'YTickMode','manual','YTick',[-180,-90,0,90,180]);gridsubplot(2,2,3);plot(w/pi,dbH);title('幅度響應(yīng)(dB)');ylabel('dB');xlabel('頻率(\pi)');axis([0,1,-60,5]);set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,0.7,0.8]);set(gca,'YTickMode','manual','YTick',[-60,-20,-1,0]);gridsubplot(2,2,4);zplane(bd,ad);axis([-1.1,1.1,-1.1,1.1]);title('零極點(diǎn)圖')n=3Omgn=1.0e+003*1.45312.7528bd=0.01150.0000-0.0344-0.00000.0344-0.0000-0.0115ad=1.0000-0.00002.1378-0.00001.76930.00000.5398三、.實(shí)驗(yàn)小結(jié)1、認(rèn)真閱讀實(shí)驗(yàn)原理，明確本次實(shí)驗(yàn)任務(wù)，讀懂例題程序，了解實(shí)驗(yàn)方