實(shí)驗(yàn)11用MATLAB設(shè)計(jì)FIR數(shù)字濾波器綜述

實(shí)驗(yàn)報(bào)告院系：信息工程學(xué)院班級(jí)：電信二班學(xué)號(hào)：課程名稱：數(shù)字信號(hào)辦理姓名：實(shí)驗(yàn)成績：日期：指導(dǎo)教師：實(shí)驗(yàn)11用MATLAB設(shè)計(jì)FIR數(shù)字濾波器一、實(shí)驗(yàn)?zāi)康模?、加深對(duì)窗函數(shù)法設(shè)計(jì)FIR數(shù)字濾波器的基來源理的理解。2、學(xué)慣用MATLAB語言的窗函數(shù)法編寫設(shè)計(jì)FIR數(shù)字濾波器的程序。3、認(rèn)識(shí)MATLAB語言相關(guān)窗函數(shù)法設(shè)計(jì)FIR數(shù)字濾波器的常用函數(shù)用法。二、實(shí)驗(yàn)內(nèi)容及步驟2、選擇適合的窗函數(shù)設(shè)計(jì)FIR數(shù)字低通濾波器，要求：wp=0.2π，Rp=0.05dB；ws=0.3π，As=40dB。描述該濾波器的脈沖響應(yīng)、窗函數(shù)及濾波器的幅頻響應(yīng)曲線和相頻響應(yīng)曲線。剖析：依據(jù)設(shè)計(jì)指標(biāo)要求，并查表11-1，選擇漢寧窗。程序清單以下：functionhd=ideal_lp(wc,N)wp=0.2*pi;ws=0.3*pi;deltaw=ws-wp;tao=(N-1)/2;n=[0:(N-1)];m=n-tao+eps;hd=sin(wc*m)./(pi*m);function[db,mag,pha,grd,w]=freqz_m(b,a);[H,w]=freqz(b,a,1000,'whole');H=(H(1:501))';w=(w(1:501))';mag=abs(H);db=20*log10((mag+eps)/max(mag));pha=angle(H);grd=grpdelay(b,a,w);wp=0.2*pi;ws=0.3*pi;deltaw=ws-wp;wc=(ws+wp)/2;第1頁共9頁N0=ceil(6.6*pi/deltaw);N=N0+mod(N0+1,2)windows=(hanning(N))';hd=ideal_lp(wc,N);b=hd.*windows;[db,mag,pha,grd,w]=freqz_m(b,1);n=0:N-1;dw=2*pi/1000;Rp=-(min(db(1:wp/dw+1)))%查驗(yàn)通帶顛簸As=-round(max(db(ws/dw+1:501)))%查驗(yàn)最小阻帶衰減subplot(2,2,1);stem(n,b);axis([0,N,1.1*min(b),1.1*max(b)]);title('實(shí)質(zhì)脈沖響應(yīng)');xlabel('n');ylabel('h(n)');subplot(2,2,2);stem(n,windows);axis([0,N,0,1.1]);title('窗函數(shù)特征');xlabel('n');ylabel('wd(n)');subplot(2,2,3);plot(w/pi,db);axis([0,1,-80,10]);title('幅度頻次響應(yīng)');xlabel('頻次（單位：\pi）');ylabel('H(e^{j\omega})');set(gca,'XTickMode','manual','XTick',[0,wp/pi,ws/pi,1]);set(gca,'YTickMode','manual','YTick',[-50,-20,-3,0]);gridsubplot(2,2,4);plot(w/pi,pha);axis([0,1,-4,4]);title('相位頻次響應(yīng)');xlabel('頻次（單位：\pi）');ylabel('\phi(\omega)');set(gca,'XTickMode','manual','XTick',[0,wp/pi,ws/pi,1]);set(gca,'YTickMode','manual','YTick',[-3.1416,0,3.1416,4]);gridN=67Rp=0.0706As=44第2頁共9頁實(shí)質(zhì)脈沖響應(yīng)窗函數(shù)特征10.2))nn((0.1d0.5hw0020406002040600nn幅度頻次響應(yīng)4相位頻次響應(yīng)03.1416-3)-20)je(0(H-50-3.14160101頻次（單位：）頻次（單位：）3、用凱塞窗設(shè)計(jì)一個(gè)FIR數(shù)字高通濾波器，要求：π；ws=0.2πwp=0.3，Rp=0.1dB，As=50dB。描述該濾波器的脈沖響應(yīng)、窗函數(shù)及濾波器的幅頻響應(yīng)曲線和相頻響應(yīng)曲線。程序清單以下：functionhd=ideal_lp(wc,N)tao=(N-1)/2;n=[0:(N-1)];m=n-tao+eps;hd=sin(wc*m)./(pi*m);function[db,mag,pha,grd,w]=freqz_m(b,a);[H,w]=freqz(b,a,1000,'whole');H=(H(1:501))';w=(w(1:501))';mag=abs(H);db=20*log10((mag+eps)/max(mag));pha=angle(H);grd=grpdelay(b,a,w);第3頁共9頁wp=0.3*pi;ws=0.2*pi;deltaw=wp-ws;N0=ceil(6.6*pi/deltaw);N=N0+mod(N0+1,2)windows=(kaiser(N,7.865))';wc=(ws+wp)/2;hd=ideal_lp(pi,N)-ideal_lp(wc,N);b=hd.*windows;[db,mag,pha,grd,w]=freqz_m(b,1);n=0:N-1;dw=2*pi/1000;Rp=-(min(db(wp/dw+1:501)))%查驗(yàn)通帶顛簸As=-round(max(db(1:ws/dw+1)))%查驗(yàn)最小阻帶衰減subplot(2,2,1);stem(n,b);axis([0,N,1.1*min(b),1.1*max(b)]);title('實(shí)質(zhì)脈沖響應(yīng)');xlabel('n');ylabel('h(n)');subplot(2,2,2);stem(n,windows);axis([0,N,0,1.1]);title('窗函數(shù)特征');xlabel('n');ylabel('wd(n)');subplot(2,2,3);plot(w/pi,db);axis([0,1,-100,2]);title('幅度頻次響應(yīng)');xlabel('頻次（單位：\pi）');ylabel('H(e^{j\omega})');set(gca,'XTickMode','manual','XTick',[0,ws/pi,wp/pi,1]);set(gca,'YTickMode','manual','YTick',[,-40-20,-3,0]);gridsubplot(2,2,4);plot(w/pi,pha);axis([0,1,-4,4]);title('相位頻次響應(yīng)');xlabel('頻次（單位：\pi）');ylabel('\phi(\omega)');set(gca,'XTickMode','manual','XTick',[0,ws/pi,wp/pi,1]);set(gca,'YTickMode','manual','YTick',[-pi,0,pi]);gridN=67Rp=0.2321第4頁共9頁As=32實(shí)質(zhì)脈沖響應(yīng)窗函數(shù)特征0.810.6)0.4)nn((0.2dhw0.50-0.2002040602040600nn幅度頻次響應(yīng)相位頻次響應(yīng)0-33.1416))je(0(H-60-3.14160101頻次（單位：）頻次（單位：）4、選擇適合的窗函數(shù)設(shè)計(jì)一個(gè)FIR數(shù)字帶通濾波器，要求：fp1=3.5kHz，fp2=6.5kHz，Rp=0.05dB；fs1=2.5kHz，fs2=7.5kHz，As=60dB。濾波器采樣頻次Fs=20kHz。描述該濾波器的脈沖響應(yīng)、窗函數(shù)及濾波器的幅頻響應(yīng)曲線和相頻響應(yīng)曲線。剖析：依據(jù)設(shè)計(jì)指標(biāo)應(yīng)選擇布萊克曼窗。程序清單以下：function[db,mag,pha,grd,w]=freqz_m(b,a);[H,w]=freqz(b,a,1000,'whole');H=(H(1:501))';w=(w(1:501))';mag=abs(H);db=20*log10((mag+eps)/max(mag));pha=angle(H);grd=grpdelay(b,a,w);fp1=3.5;fp2=6.5;fs1=2.5;fs2=7.5;Fs=20;ws1=fs1/(Fs/2)*pi;ws2=fs2/(Fs/2)*pi;第5頁共9頁wp1=fp1/(Fs/2)*pi;wp2=fp2/(Fs/2)*pi;deltaw=wp1-ws1;N0=ceil(11*pi/deltaw);N=N0+mod(N0+1,2)%為實(shí)現(xiàn)FIR種類1偶對(duì)稱濾波器，應(yīng)保證N為奇數(shù)windows=blackman(N);wc1=(ws1+wp1)/2/pi;wc2=(ws2+wp2)/2/pi;b=fir1(N-1,[wc1,wc2],windows);[db,mag,pha,grd,w]=freqz_m(b,1);n=0:N-1;dw=2*pi/1000;Rp=-(min(db(wp1/dw+1:wp2/dw+1)))%查驗(yàn)通帶顛簸ws0=[1:ws1/dw+1,ws2/dw+1:501];%成立阻帶頻次樣點(diǎn)數(shù)組As=-round(max(db(ws0)))%查驗(yàn)最小阻帶衰減subplot(2,2,1);stem(n,b);axis([0,N,1.1*min(b),1.1*max(b)]);title('實(shí)質(zhì)脈沖響應(yīng)');xlabel('n');ylabel('h(n)');subplot(2,2,2);stem(n,windows);axis([0,N,0,1.1]);title('窗函數(shù)特征');xlabel('n');ylabel('wd(n)');subplot(2,2,3);plot(w/pi,db);axis([0,1,-150,10]);title('幅度頻次響應(yīng)');xlabel('頻次（單位：\pi）');ylabel('H(e^{j\omega})');set(gca,'XTickMode','manual','XTick',[0,fs1,fp1,fp2,fs2,500]);set(gca,'YTickMode','manual','YTick',[-150,-40,-3,0]);gridsubplot(2,2,4);plot(w/pi,pha);axis([0,1,-4,4]);title('相位頻次響應(yīng)');xlabel('頻次（單位：\pi）');ylabel('\phi(\omega)');set(gca,'XTickMode','manual','XTick',[0,fs1,fp1,fp2,fs2,500]);set(gca,'YTickMode','manual','YTick',[-pi,0,pi]);grid=111Rp=0.0034As=74第6頁共9頁實(shí)質(zhì)脈沖響應(yīng)窗函數(shù)特征0.41)0.2)nn((d0.5h0w-0.20501000501000nn幅度頻次響應(yīng)相位頻次響應(yīng)03.1416-3)-40)je(0(H-150-3.141600頻次（單位：）頻次（單位：）5、選擇適合的窗函數(shù)設(shè)計(jì)一個(gè)FIR數(shù)字帶阻濾波器，要求：f=1kHz，fp2=4.5kHz，p1Rp=0.1dB；fs1=2kHz，fs2=3.5kHz，As=40dB。濾波器采樣頻次Fs=10kHz。描述該濾波器的脈沖響應(yīng)、窗函數(shù)及濾波器的幅頻響應(yīng)曲線和相頻響應(yīng)曲線。剖析：依據(jù)設(shè)計(jì)指標(biāo)選擇漢寧窗。程序清單以下：functionhd=ideal_lp(wc,N)tao=(N-1)/2;n=[0:(N-1)];m=n-tao+eps;hd=sin(wc*m)./(pi*m);function[db,mag,pha,grd,w]=freqz_m(b,a);[H,w]=freqz(b,a,1000,'whole');H=(H(1:501))';w=(w(1:501))';mag=abs(H);db=20*log10((mag+eps)/max(mag));pha=angle(H);第7頁共9頁grd=grpdelay(b,a,w);fp1=1;fp2=4.5;fs1=2;fs2=3.5;Fs=10;ws1=fs1/(Fs/2)*pi;ws2=fs2/(Fs/2)*pi;wp1=fp1/(Fs/2)*pi;wp2=fp2/(Fs/2)*pi;wp=[wp1,wp2];ws=[ws1,ws2];deltaw=ws1-wp1;N0=ceil(6.2*pi/deltaw);N=N0+mod(N0+1,2)%為實(shí)現(xiàn)FIR種類1偶對(duì)稱濾波器，應(yīng)保證N為奇數(shù)windows=(hanning(N))';wc1=(ws1+wp1)/2;wc2=(ws2+wp2)/2;hd=ideal_lp(wc1,N)+ideal_lp(pi,N)-ideal_lp(wc2,N);%成立理想帶阻b=hd.*windows;[db,mag,pha,grd,w]=freqz_m(b,1);n=0:N-1;dw=2*pi/1000;wp0=[1:wp1/dw+1,wp2/dw+1:501];%成立通帶頻次樣點(diǎn)數(shù)組As=-round(max(db(ws1/dw+1:ws2/dw+1)))%查驗(yàn)最小阻帶衰減Rp=-(min(db(wp0)))%查驗(yàn)通帶顛簸subplot(2,2,1);stem(n,b);axis([0,N,1.1*min(b),1.1*max(b)]);title('實(shí)質(zhì)脈沖響應(yīng)');xlabel('n');ylabel('h(n)');subplot(2,2,2);stem(n,windows);axis([0,N,0,1.1]);title('窗函數(shù)特征');xl