Matlab課程設(shè)計利用MATLAB結(jié)合雙線性變換法設(shè)計數(shù)字

1、開始讀入數(shù)字濾波器技術(shù)指標(biāo)將指標(biāo)轉(zhuǎn)換成歸一化模擬低通濾波器的指標(biāo)設(shè)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(zhuǎn)換成數(shù)字帶通濾波器H(z輸入信號后顯示相關(guān)結(jié)果求相應(yīng)的幅頻響應(yīng)與相頻響應(yīng) 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10203040-0.01-0.00500.0050.01ty濾波器輸出y 的波形clc;clear all ;結(jié)束%數(shù)字濾波器的技術(shù)指標(biāo)Rp = 1; % 通帶最大衰減Rs = 40;%

2、阻帶最小衰減OmegaS1_1=350; % 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

3、換OmegaS2=2*Fp*tan(Ws2/2; % 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(zhuǎn)換成低通參數(shù)Lemta_S1_

4、EquivalentLowPass=-Eta_S1/(Eta_S12-Eta_P02; % 轉(zhuǎn)換成低通參數(shù)Lemta_S2_EquivalentLowPass=Eta_S2/(Eta_S22-Eta_P02; % 轉(zhuǎn)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

5、9;% 濾波器設(shè)計num1,den1=cheby2(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(zhuǎn)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(zhuǎn)換為帶通濾波器% 計算增益響應(yīng)w = 0:pi/255:pi;h = freqz(num,den,w;g = 20*log10(a

6、bs(h;%繪制切比雪夫帶通濾波器幅頻特性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(yīng)'%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

7、+x2;figure;subplot(2,2,1%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;xlab

8、el('t'ylabel('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(shè)計IIR數(shù)字帶通濾波器例21-3采用雙線性變換法設(shè)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

9、=1 dB;阻帶ws1=0.2p,ws2=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*Omgs

10、2; %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(shè)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+e

11、ps/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

12、,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'axis(

13、0,Fs/2,-40,5;ylabel('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(jié)果如下:n = 3Omgn =1.0e+

14、003 * 1.0191 3.9252bd =0.0736 0.0000 -0.2208 0.0000 0.2208 -0.0000 -0.0736ad =1.0000 0.0000 0.9761 0.0000 0.8568 0.0000 0.2919 采用雙線性變換法設(shè)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(shè)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(shè)計指標(biāo)的。程序運行結(jié)果如下:n = 3Omgn = 1.0e+003 *0.66416.0234bd = 0.2537 0.0000 -0.4733 0.0000 0.4733 0.0000 -0.2537ad =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(shè)計切比雪夫型帶通數(shù)字濾波器由程序數(shù)據(jù)和