實(shí)驗(yàn)：用雙線(xiàn)性變換法設(shè)計(jì)IIR數(shù)字濾波器.doc

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實(shí)驗(yàn)三：用雙線(xiàn)性變換法設(shè)計(jì)IIR數(shù)字濾波器（設(shè)計(jì)性 4學(xué)時(shí)）一.實(shí)驗(yàn)?zāi)康模?1）熟悉用雙線(xiàn)性變換法設(shè)計(jì)IIR數(shù)字濾波器的原理與方法。(2）掌握數(shù)字濾波器的計(jì)算機(jī)仿真方法。(3）通過(guò)觀(guān)察對(duì)實(shí)際心電圖信號(hào)的濾波作用，獲得數(shù)字濾波的感性知識(shí)。 二.實(shí)驗(yàn)內(nèi)容及步驟:(1) 用雙線(xiàn)性變換法設(shè)計(jì)一個(gè)巴特沃斯低通IIR數(shù)字濾波器，設(shè)計(jì)指標(biāo)參數(shù)為：在通帶內(nèi)頻率低于0.2pi時(shí),最大衰減小于1dB;在阻帶內(nèi)0.3pi , pi 頻率區(qū)間上，,最小衰減大于15dB；(2) 以 0.02pi為采樣間隔，打印出數(shù)字濾波器在頻率區(qū)間 0, 0.5pi上的幅頻響應(yīng)特性曲線(xiàn)；(3) 用所設(shè)計(jì)的濾波器對(duì)實(shí)際心電圖信號(hào)采樣序列(在本實(shí)驗(yàn)后面給出)進(jìn)行仿真濾波處理，并分別打印出濾波前后的心電圖波形圖，觀(guān)察總結(jié)濾波作用與效果。（4）采用不同階數(shù)的Butterworth 低通濾波器，比較濾波效果。三.實(shí)驗(yàn)步驟：（1）復(fù)習(xí)有關(guān)巴特沃斯模擬濾波器設(shè)計(jì)和用雙線(xiàn)性變換法設(shè)計(jì)IIR數(shù)字濾波器的內(nèi)容，按照教材例6.4.2，用雙線(xiàn)性變換法設(shè)計(jì)數(shù)字濾波器系統(tǒng)函數(shù)H（z）。方法一：教材例6.4.2種已求出滿(mǎn)足本實(shí)驗(yàn)要求的數(shù)字濾波器系統(tǒng)函數(shù)：方法二：根據(jù)設(shè)計(jì)指標(biāo)，調(diào)用MATLAB信號(hào)處理工具箱函數(shù)buttord和butter，也可得到H（z）。（2）編寫(xiě)濾波器仿真程序，計(jì)算H(z)對(duì)心電圖信號(hào)采樣序列x(n)的相應(yīng)序列y(n)。（3）在通過(guò)計(jì)算機(jī)上運(yùn)行仿真濾波程序，并調(diào)用通用繪圖子程序，完成實(shí)驗(yàn)內(nèi)容（2）和（3）。本實(shí)驗(yàn)要用的MATLAB繪圖函數(shù)參閱教材。四.,思考題:用雙線(xiàn)性變換法設(shè)計(jì)數(shù)字濾波器過(guò)程中,變換公式：s=中T的取值,對(duì)設(shè)計(jì)結(jié)果有無(wú)影響? 為什么? 五.實(shí)驗(yàn)報(bào)告要求（1）簡(jiǎn)述實(shí)驗(yàn)?zāi)康募霸?；?）由所打印的特性曲線(xiàn)及設(shè)計(jì)過(guò)程簡(jiǎn)述雙線(xiàn)性變換法的特點(diǎn)；（3）對(duì)比濾波前后的心電圖信號(hào)波形,說(shuō)明數(shù)字濾波器的濾波過(guò)程與濾波作用； (4) 簡(jiǎn)要回答思考題.六:心電圖信號(hào)采樣序列 x(n)：人體心電圖信號(hào)在測(cè)量過(guò)程中往往受到工業(yè)高頻干擾，所以必須經(jīng)過(guò)低通濾波處理后，才能作為判斷心臟功能的有用信息。下面給出一實(shí)際心電圖信號(hào)采樣序列樣式本x(n)，其中存在高頻干擾，在實(shí)驗(yàn)中，以x(n)作為輸入序列，濾除其中的干擾成分。 x(n) = -4 , -2, 0, -4, -6, -4, -2, -4, -6, -6, -4, -4, -6, -6, -2, 6, 12, 8, 0, -16 -38, -60, -84, -90, -66, -32, -4, -2, -4, 8，12, 12 , 10, 6, 6, 6, 4, 0, 0, 0 0, 0, -2, -4, 0, 0, 0, -2, -2, 0，0 , -2, -2, -2, -2, 0參考程序：一；T=1;Fs=1/T;wpz=0.2;wsz=0.3;wp=2*tan(wpz*pi/2);ws=2*tan(wsz*pi/2);rp=1;rs=15;N,wc=buttord(wp,ws,rp,rs,s);B,A=butter(N,wc,s);fk=0:1/512:1;wk=2*pi*fk;Hk=freqs(B,A,wk);subplot(2,2,1);plot(fk,20*log10(abs(Hk);grid on;xlabel(omega/pi);ylabel(幅度(dB);axis(0,1,-100,5);title(b);N,wc=buttord(wpz,wsz,rp,rs);Bz,Az=butter(N,wc);wk=0:pi/512:pi;Hz=freqz(Bz,Az,wk);subplot(2,2,4);plot(wk/pi,20*log10(abs(Hz);grid on;xlabel(omega/pi);ylabel(幅度(dB);axis(0,1,-100,5);title(b); 二；x=-4,-2,0,-4,-6,-4,-2,-4,-6,-6,-4,-4,-6,-6,-2,6,12,8,0,-16,-38,-60,-84,-90,-66,-32,-4,-2,-4,8,12,12,10,6,6,6,4,0,0,0,0,0,-2,-4,0,0,0,-2,-2,0,0,-2,-2,-2,-2,0;subplot(2,2,1);n=0:55;stem(n,x,.);xlabel(n);ylabel(x(n);title(x(n)的脈沖響應(yīng));A=0.09036;b1=A,2*A,A;a1=1,-1.2686,0.7051;h1=filter(b1,a1,x);H1,w=freqz(b1,a1,100);b2=A,2*A,A;a2=1,-1.0106,0.3583;h2=filter(b2,a2,h1);H2,w=freqz(b2,a2,100);b3=A,2*A,A;a3=1,-0.9044,0.2155;h3=filter(b3,a3,h2);H3,w=freqz(b3,a3,100);subplot(2,2,2);stem(n,h3,.);xlabel(n);ylabel(y(n);title(通過(guò)濾波器H1(z),H2(z),H3(z)后的y3(n)函數(shù));subplot(2,2,3);H4=H1.*(H2);H=H4.*(H3);mag=abs(H);db=20*log10(mag+eps)/max(mag);plot(w/pi,db);xlabel(/);ylabel(20logHa3(ejw);title(通過(guò)濾波器H1(z),H2(z),H3(z)后的對(duì)數(shù)頻率響應(yīng)20logHa3(ejw)函數(shù));grid;figure(2);N=1024;n=0:N/2-1;Xk=fft(x,N);AXk=abs(Xk(1:N/2);f=(0:N/2-1)*Fs/N;f=f/Fs;subplot(211);plot(f,AXk);title(x(n)的頻譜);xlabel(f);ylabel(| X(k) |);axis(0,0.5,0,400);Yk=fft(y,N);AYk=abs(Yk(1:N/2);subplot(212);plot(f,AYk);title(y(n)的頻譜);xlabel(f);ylabel(| Y(k) |);axis(0,0.5,0,400)x=-4,-2,0,-4,-6,-4,-2,-4,-6,-6,-4,-4,-6,-6,-2,6,12,8,0,-16,-38,-60,-84,-90,-66,-32,-4,-2,-4,8,12,12,10,6,6,6,4,0,0,0,0,0,-2,-4,0,0,0,-2,-2,0,0,-2,-2,-2,-2,0;subplot(2,2,1);n=0:55;stem(n,x,.);xlabel(n);ylabel(x(n);title(x(n)的脈沖響應(yīng));A=0.09036;b1=A,2*A,A;a1=1,-1.2686,0.7051;h1=filter(b1,a1,x);H1,w=freqz(b1,a1,100);b2=A,2*A,A;a2=1,-1.0106,0.3583;h2=filter(b2,a2,h1);H2,w=freqz(b2,a2,100);b3=A,2*A,A;a3=1,-0.9044,0.2155;h3=filter(b3,a3,h2);H3,w=freqz(b3,a3,100);subplot(2,2,2);stem(n,h3,.);xlabel(n);ylabel(y(n);title(通過(guò)濾波器H1(z),H2(z),H3(z)后的y3(n)函數(shù));subplot(2,2,3);H4=H1.*(H2);H=H4.*(H3);mag=abs(H);db=20*log10(mag+eps)/max(mag);plot(w/pi,db);xlabel(/);ylabel(20logHa3(ejw);title(通過(guò)濾波器H1(z),H2(z),H3(z)后的對(duì)數(shù)頻率響應(yīng)20logHa3(ejw)函數(shù));grid;%x(n)的心電脈沖函數(shù)x=-4,-2,0,-4,-6,-4,-2,-4,-6,-6,-4,-4,-6,-6,-2,6,12,8,0,-16,-38,-60,-84, -90,-66,-32,-4,-2,-4,8,12,12,10,6,6,6,4,0,0,0,0,0,-2,-4,0,0,0,-2,-2,0,0,-2,-2,-2,-2,0subplot(2,2,1);n=0:55;stem(n,x,.);xlabel(n);ylabel(x(n);title(x(n)的心電脈沖函數(shù));%通過(guò)濾波器H1(z)后的y1(n)函數(shù)A=0.09036;b1=A,2*A,A;a1=1,-1.2686,0.7051;h1=filter(b1,a1,x);H1,w=freqz(b1,a1,100);%通過(guò)濾波器H1(z),H2(Z)后的y2(n)函數(shù)b2=A,2*A,A;a2=1,-1.0106,0.3583;h2=filter(b2,a2,h1);H2,w=freqz(b2,a2,100);%通過(guò)濾波器H1(z),H2(Z),H3(Z)后的y3(n)函數(shù)b3=A,2*A,A;a3=1,-0.9044,0.2155;h3=filter(b3,a3,h2);H3,w=freqz(b3,a3,100);subplot(2,2,2);stem(n,h3,.);xlabel(n);ylabel(y(n);title(通過(guò)濾波器H1(Z),H2(Z),H3(Z)后的y3(n)函數(shù));subplot(2,2,3);H4=H1.*(H2);H=H4.*(H3);mag=abs(H);db=20*log10(mag+eps)/max(mag);plot(w/pi,db);xlabel(w/pi);ylabel(20logHa3(ejw);title(通過(guò)濾波器H1(z)、H2(z)、H3(z)后的對(duì)數(shù)頻率響應(yīng)20logHa3(ejw)函數(shù));grid;