用双线性变换法设计切比雪夫II型的数字IIR带通滤波器

用线换设比夫II的数IIR通波器

t)t)xt)(t)sin(2t)sin(2t1fy(t)1II

I用线换设型通比夫II的IIR滤器要带界为400Hz，500Hz，带频分350Hz，带最衰带衰抽频2000Hz，MATLAB画出频性画分滤传函零点信号过该滤器其450Hz，，波的输是什么用Matlab你的论给的形(t),(t),x(t),()12Matlab详细设计：%DesignofaChebIIBandpassDigitalFilterusingbilinearmethodclc;clearRp=%bandpassattenuationindBRs=%bandstopattenuationindBOmegaS1_1=350;OmegaS1_2=550;OmegaP1_1=400;OmegaP1_2=500;Fp=2000;%samlingfrequencyWp1=2*pi*OmegaP1_1/Fp;Wp2=2*pi*OmegaP1_2/Fp;Ws1=2*pi*OmegaS1_1/Fp;Ws2=2*pi*OmegaS1_2/Fp;OmegaP1=2*Fp*tan(Wp1/2);%nonlinearlizationOmegaP2=2*Fp*tan(Wp2/2);%nonlinearlizationOmegaS1=2*Fp*tan(Ws1/2);%nonlinearlizationOmegaS2=2*Fp*tan(Ws2/2);%nonlinearlizationOmegaP0=sqrt(OmegaP1*OmegaP2);equivalentmidfrequencyBw=OmegaP2-OmegaP1;%bandwithEta_P0=OmegaP0/Bw;%NormalizationEta_P1=OmegaP1/Bw;%NormalizationEta_P2=OmegaP2/Bw;%NormalizationEta_S1=OmegaS1/Bw;%NormalizationEta_S2=OmegaS2/Bw;%NormalizationLemta_P_EquivalentLowPass=Eta_P2/(Eta_P2^2-Eta_P0^2);%changetothe

equivalentLowpasspatameterLemta_S1_EquivalentLowPass=-Eta_S1/(Eta_S1^2-Eta_P0^2);%changetheequivalentLowpasspatameterLemta_S2_EquivalentLowPass=Eta_S2/(Eta_S2^2-Eta_P0^2);changetotheequivalentLowpasspatameterLemta_S_EquivalentLowPass=min(Lemta_S1_EquivalentLowPass,Lemta_S2_EquivalentLowPass);%getthesmallest%EstimatetheFilterOrder[N,Wn]=cheb2ord(Lemta_P_EquivalentLowPass,Lemta_S_EquivalentLowPass,Rp,Rs,'s');%DesigntheFilter[num1,den1]=cheby2(N,Rs,Wn,'s');[num2,den2]=lp2bp(num1,den1,OmegaP0,Bw);[num,den]=bilinear(num2,den2,Fp);%Computethegainresponsew=0:pi/255:pi;h=freqz(num,den,w);g=20*log10(abs(h));%Plotthegainresponsefigure;plot(w/pi,g);gridaxis([01-605]);xlabel('\omega/\pi');ylabel('GainindB');title('GainResponseofaChebBandpass);%Plotthepolesandzeros[z,p,k]=tf2zp(num,den);figure;zplane(z,p);%»æÖÆ´«Ê亯ÊýÁ㼫µãtitle('´«Ê亯ÊýµÄÁ㼫µã')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(2,2,1)%»æÖÆx1µÄ²¨ÐÎplot(x1);gridon;axis([0,50*pi,-3,3]);xlabel('t');ylabel('x1(t)'title('x1µÄ²¨ÐÎ');subplot(2,2,2)%»æÖÆx1µÄ²¨ÐÎplot(x2);gridon;axis([0,50*pi,-3,3]);xlabel('t');ylabel('x2(t)'

title('x2µÄ²¨ÐÎ');subplot(2,2,3)%»æÖÆÊäÈëxµÄ²¨ÐÎplot(x);gridonaxis([0,50*pi,-3,3]);xlabel('t');ylabel('x(t)'title()%X=fft(x);y=filter(num,den,x);%Êý×ÖÂ˲¨Æ÷Êä³ösubplot(2,2,4);%»æÖÆÊä³öyµÄ²¨ÐÎplot(real(y));gridonaxis([0,50*pi,-3,3]);xlabel('t');ylabel();title('Â˲¨Æ÷Êä³öyµÄ²¨ÐÎ');测试结果：图

实程图运行结如下：

itrriitrriGainFilteri

0-10-20-30-40-50-60

00.20.30.40.60.70.80.9/

传输函数的零极点I

10.80.60.40.20-1-1-0.5