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1、巴特沃兹模拟滤波器的MATLAB实现设计一个模拟巴特沃特低通滤波器，它在30rad/s处具有1dB或更好的波动，在50rad/s处具有至少30dB的衰减。求出级联形式的系统函数，画出滤波器的幅度响应、对数幅度响应、相位响应和脉冲响应图。解：程序清单如下Wp=30;Ws=50;Rp=1;As=30;%技术指标Ripple=10^(-Rp/20);Attn=10^(-As/20);[b,a]=afd_butt(Wp,Ws,Rp,As)%巴特沃兹低通滤波器[C,B,A]=sdir2cas(b,a)%计算二阶节系数,级联型实现[db,mag,pha,w]=freqs_m(
2、b,a,50);%计算幅频响应[ha,x,t]=impulse(b,a);%计算模拟滤波器的单位脉冲响应figure(1);clf;subplot(2,2,1);plot(w,mag);title('MagnitudeResponse');xlabel('Analogfrequencyinrad/s');ylabel('H');%axis([0,50,0,1.1])set(gca,'XTickMode','manual','XTick',[0,30,40,50]);set(gca,'YTickMode','manual','YTick',[0,Attn,Rippl
3、e,1]);gridsubplot(2,2,2);plot(w,db);title('MagnitudeindB');xlabel('Analogfrequencyinrad/s');ylabel('decibels');%axis([0,50,-40,5])set(gca,'XTickMode','manual','XTick',[0,30,40,50]);set(gca,'YTickMode','manual','YTick',[-40,-As,-Rp,0]);gridsubplot(2,2,3);plot(w,pha/pi);title('PhaseResp
4、onse');xlabel('Analogfrequencyinrad/s');ylabel('radians');%axis([0,50,-1.1,1.1])set(gca,'XTickMode','manual','XTick',[0,30,40,50]);set(gca,'YTickMode','manual','YTick',[-1,-0.5,0,0.5,1]);gridsubplot(2,2,4);plot(t,ha);title('ImpulseResponse');xlabel('timeinseconds');ylabel('ha(t)');axi
5、s([0,max(t)+0.05,min(ha),max(ha)+0.025]);set(gca,'XTickMode','manual','XTick',[0,0.1,max(t)]);set(gca,'YTickMode','manual','YTick',[0,0.1,max(ha)]);grid%巴特沃兹模拟滤波器的设计子程序function[b,a]=afd_butt(Wp,Ws,Rp,As);ifWp<=0error('Passbandedgemustbelargerthan0')endifWs<=Wperror('Stopbandedgemustbe
6、largerthanPassededge')endif(Rp<=0)
7、(As<0)error('PBrippleand/0rSBattenuationmustbelargerthan0')endN=ceil((log10((10^(Rp/10)-1)/(10^(As/10)-1)))/(2*log10(Wp/Ws)));OmegaC=Wp/((10^(Rp/10)-1)^(1/(2*N)));[b,a]=u_buttap(N,OmegaC);%设计非归一化巴特沃兹模拟低通滤波器原型子程序function[b,a]=u_buttap(N,OmegaC);[z,p,k
8、]=buttap(N);p=p*OmegaC;k=k*OmegaC^N;B=real(poly(z));b0=k;b=k*B;a=real(poly(p));%计算系统函数的幅度响应和相位响应子程序function[db,mag,pha,w]=freqs_m(b,a,wmax);w=[0:1:500]*wmax/500;H=freqs(b,a,w);mag=abs(H);db=20*log10((mag+eps)/max(mag));pha=angle(H);%直接形式转换成级联形式子程序function[C,B,A]=sdir2cas(b,a);Na=lengt
9、h(a)-
