Matlab課程設計利用MATLAB結合雙線性變換法設計數(shù)字切比雪夫帶通IIR濾波器代碼

1、開始讀入數(shù)字濾波器技術指標將指標轉換成歸一化模擬低通濾波器的指標設計歸一化的模擬低通濾波器階數(shù)N 和截止頻率模擬域頻率變換,將H(P變換成模擬帶通濾波器H(s用雙線性變換法將H(s轉換成數(shù)字帶通濾波器H(z輸入信號后顯示相關結果求相應的幅頻響應與相頻響應 50100150-202tx 1(t x1的波形50100150-202tx 2(t x2的波形 50100150-202t x (t 輸入信號x 的波形10203040ty濾波器輸出y 的波形clc;clear all ;結束%數(shù)字濾波器的技術指標Rp = 1; % 通帶最大衰減Rs = 40;% 阻帶最小衰減OmegaS1_1=350;

2、% 通帶截止頻率OmegaS1_2=550;% 通帶截止頻率OmegaP1_1=400; % 阻帶截止頻率OmegaP1_2=500;% 阻帶截止頻率Fp=2000; % 抽樣頻率Wp1=2*pi*OmegaP1_1/Fp; % 模數(shù)頻率變換Wp2=2*pi*OmegaP1_2/Fp;Ws1=2*pi*OmegaS1_1/Fp;Ws2=2*pi*OmegaS1_2/Fp;OmegaP1=2*Fp*tan(Wp1/2; % 非線性變換OmegaP2=2*Fp*tan(Wp2/2; % 非線性變換OmegaS1=2*Fp*tan(Ws1/2; % 非線性變換OmegaS2=2*Fp*tan(Ws2

3、/2; % 非線性變換OmegaP0=sqrt(OmegaP1*OmegaP2;% 等效中心頻率Bw=OmegaP2-OmegaP1; % 帶通濾波器的通帶寬度Eta_P0=OmegaP0/Bw; % 歸一化處理Eta_P1=OmegaP1/Bw; % 歸一化處理Eta_P2=OmegaP2/Bw; % 歸一化處理Eta_S1=OmegaS1/Bw; % 歸一化處理Eta_S2=OmegaS2/Bw; % 歸一化處理Lemta_P_EquivalentLowPass=Eta_P2/(Eta_P22-Eta_P02; % 轉換成低通參數(shù)Lemta_S1_EquivalentLowPass=-Et

4、a_S1/(Eta_S12-Eta_P02; % 轉換成低通參數(shù)Lemta_S2_EquivalentLowPass=Eta_S2/(Eta_S22-Eta_P02; % 轉換成低通參數(shù)Lemta_S_EquivalentLowPass=min(Lemta_S1_EquivalentLowPass,Lemta_S2 _EquivalentLowPass; % 取最小值% E求濾波器階數(shù)N, Wn=cheb2ord(Lemta_P_EquivalentLowPass, Lemta_S_EquivalentLowPass, Rp, Rs,'s'% 濾波器設計num1,den1=ch

5、eby2(N,Rs,Wn,'s'num2,den2=lp2bp(num1,den1,OmegaP0,Bw;num,den=bilinear(num2,den2,Fp;Z,P,K=cheb1ap(N,Rp;w=linspace(1,1000,100*2*pi;M1,N1=zp2tf(Z,P,K; %將零極點形式轉換為傳輸函數(shù)形式M,N=lp2bp(M1,N1,OmegaP0,Bw; %對低通濾波器進行頻率變換轉換為帶通濾波器% 計算增益響應w = 0:pi/255:pi;h = freqz(num,den,w;g = 20*log10(abs(h;%繪制切比雪夫帶通濾波器幅頻特性

6、figure;plot(w/pi,g;gridaxis(0 1 -60 5;xlabel('頻率/pi' ylabel('增益/dB' title('切比雪夫II型帶通濾波器幅頻響應'%Plot the poles and zerosz,p,k=tf2zp(num,den;figure;zplane(z,p; %繪制傳輸函數(shù)零極點title('?傳輸函數(shù)的零極點'f1=450;f2=600;t=0:0.0001:1x1=sin(2*pi*f1*t;x2=sin(2*pi*f2*t;x=x1+x2;figure;subplot(2,

7、2,1%繪制x1的波形plot(x1;grid on;axis(0,50*pi,-3,3;xlabel('t'ylabel('x1(t'title('x1的波形'subplot(2,2,2%繪制x2的波形plot(x2;grid on;axis(0,50*pi,-3,3;xlabel('t'ylabel('x2(t'title('x2的波形'subplot(2,2,3%繪制輸入x的波形plot(x;grid on;axis(0,50*pi,-3,3;xlabel('t'ylabel(

8、'x(t'title('輸入信號x的波形'%X=fft(x;y=filter(num,den,x;%數(shù)字濾波器輸出subplot(2,2,4;plot(real(y;grid on;axis(0,15*pi,-0.01,0.01;xlabel('t'ylabel('y'title('濾波器輸出y的波形' 附錄:PPpppp5. 用雙線性變換法設計IIR數(shù)字帶通濾波器例21-3采用雙線性變換法設計一個切比雪夫型數(shù)字帶通濾波器,要求:通帶wp1=0.3p,wp2=0.7p,Rp=1 dB;阻帶ws1=0.2p,ws2=

9、0.8p,As=20 dB 解程序如下:wp1=0.4*pi;wp2=0.5*pi;ws1=0.35*pi;ws2=0.55*pi;Rp=1;As=40;T=0.0005;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;bw=Omgs2-Omgs1;w0=sqrt(Omgs1*Omgs2; %ZK(模擬濾波器阻帶帶寬和中心頻率

10、n,Omgn=cheb2ord(Omgp,Omgs,Rp,As,'s' %計算階數(shù)n和截止頻率z0,p0,k0=cheb2ap(n,As; %設計歸一化的模擬原型濾波器n,Omgn=cheb1ord(Omgp,Omgs,Rp,As,'s'z0,p0,k0=cheb1ap(n,Rp;ba1=k0*real(poly(z0;aa1=real(poly(p0;ba,aa=lp2bp(ba1,aa1,w0,bw;bd,ad=bilinear(ba,aa,FsH,w=freqz(bd,ad;dbH=20*log10(abs(H+eps/max(abs(H;subplot(

11、2,2,1,plot(w/2/pi*Fs,abs(H,'k'ylabel('|H|'title('幅度響應'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,'

12、k'ylabel('phi'title('相位響應'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( dB'axis(0,Fs/2,-40,5;ylabel(&

13、#39;dB'xlabel('頻率(pi'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('零極圖'程序運行結果如下:n = 3ad =1.0000 0.0000 0.9761 0.0000

14、0.8568 0.0000 0.2919 采用雙線性變換法設計一個切比雪夫型數(shù)字帶通濾波器,其它條件不變,則需要修改下面幾句程序:bw=Omgs2-Omgs1;w0=sqrt(Omgs1*Omgs2; %ZK(模擬濾波器阻帶帶寬和中心頻率n,Omgn=cheb2ord(Omgp,Omgs,Rp,As,'s' %計算階數(shù)n和截止頻率z0,p0,k0=cheb2ap(n,As; %設計歸一化的模擬原型濾波器采用阻帶截止頻率來計算W0和BW,是因為切比雪夫型模擬低通原型是以阻帶衰減As為主要設計指標的。程序運行結果如下:n = 3Omgn = 1.0e+003 *ad =1.0000 -0.0000 0.0008 0.0000 0.4206 -0.0000 -0.0343 頻率特性及零極點圖形如圖21-4所示。圖21-4 用雙線性變換法設計切比雪夫型帶通數(shù)字濾波器由程序數(shù)據(jù)和曲線可知,該設計結