03DSP研究性学习报告数字滤波器设计.docx
她京交通乂学数字信号处理课程探讨性学习报告姓名学号同组成员指导老师时间数字滤波器设计【研讨题目】基本题1.IIR数字滤波器设计设计一个IlR数字低通滤波器，其能取代下列指标的模拟低通滤波器(系统的抽样频率为44.1kHz)p=2kHz,A=IOkHZ,Ap=0.5dB,As=50dB(1)分别用双线性变换和冲激响应不变法设计一个BW型数字低通滤波器，并进行比较。(2)用双线性变换分别设计ChebyshevI型ChebyshevII型和椭圆型数字低通滤波器，并进行比较。【温磬提示】在数字滤波器的设计中，不管是用双线性变换法还是冲激响应不变法，其中的参数T的取值对设计结果没有影响。但若所设计的数字滤波器要取代指定的模拟滤波器时，则抽样频率(或抽样间隔T)将对设计结果有影响。【设计步骤】一、脉冲响应不变法1 .将数字滤波器的频率指标Q转换为模拟滤波器的频率指标皿2 .由模拟滤波器的指标设计模拟滤波器的“。模拟带通滤波器的设计步骤：(1)由带通漉波器的上下截频确定变换式中的参数B=p2-<pl届=GPeP2确定原型低通滤波器的通带截频22(3)设计通带截频为1(田出s)、阻带截频为69S、通带衰减为APdB、阻带衰减为ASdB的原型低通滤波器(4)将原型低通滤波器转换为带通滤波器，BMS)+啸Bs“BP(三)="l_+23 .利用脉冲响应不变法，将H(三)转换”(z)。二、双线性变换法1 .将数字滤波器的频率指标Q转换为模拟滤波器的频率指标皿2 .由模拟滤波器的指标设计模拟滤波器的H(三)O模拟带通滤波器的设计步骤：(1)由带通滤波器的上下截频确定变换式中的参数B=p2-就=OPeP2确定原型低通滤波器的通带截频22(3)设计通带截频为1(rad/s)、阻带截频为、通带衰减为dB、阻带衰减为ASdB的原型低通滤波器(4)将原型低通滤波器转换为带通滤波器，BMS)Hw(三)=Hl(三)_y2+fl23 .利用双线性变换法，将，(三)转换”。"(Z)=H(三)2-x-n+z1【仿真结果】所设计滤波器的幅度响应和相位响应BW型、ChebyshevI型、Chebyshev11型和椭圆型滤波器的零极点分布【结果分析】双线性变换和冲激响应不变法所设计的滤波器的性能有什么不同。BW型、ChebyshevI型、ChebyshevI1型和椭圆型滤波器的零极点分布各有什么特点。clearall;脉冲响应不变法:wp=2000*2*pi;ws=10000*2*pi;Fs=44100;Wp=wpFs;Ws=wsFs;Ap=O.5;As=50;N=buttord(wp,ws,Ap,As,s,);fprintf(,N=%.0fn,zN)wc=wp(10(0.1*Ap)-1)(1N2);numazdena=butter(N,wc,s,);nmdzdend=impinvar(nmazdena,Fs)；W=Iinspace(0zpi,2048);h=freqz(numdzdend,w);norm=max(abs（三）);numd=numdnorm;figure(1);zplane(numazdena);figure(2);plot(wpi,20*logl0(abshnorm);xlabel(,Normalizedfrequency,);ylabel(,Gain,dB,);w=WpWs;h=freqz(numdzdend,w);fprintf(,Ap=%.4fn,-20*IoglO(bs(h(l);fprintf('As=%.4fn,-20*IoglO(bs(h(2);gridon;11HgWe1UEECI6。UJ一双线性变更法：clearall;wp=2000*2*pi;ws=10000*2*pi;Fs=44100;Wp=wpFs;Ws=wsFs;Ap=O.5;As=50;N=buttord(wp,wszAp,As,s,);fprintf(,N=%.0fnN)wc=wp(10(0.1*Ap)-1)(1N2);numazdena=butter(N,wc,s,);nmdzdend=bilinear(nmazdena,Fs)；W=Iinspace(O,pi,2048);h=freqz(numd,dend,w);norm=max(abs（三）);numd=numdnorm;figure(1);zplane(numazdena);figure(2);plot(wpi,20*logl0(abs(hnorm)xlabel(,Normalizedfrequency,);ylabel(,Gain,dB,);w=WpWs;h=freqz(numdzdend,w);fprintf('Ap=%.4fn',-20*IoglO(bs(h(l);fprintf('As=%.4fn',-20*IoglO(bs(h(2);gridon;DFigIre1252-15-1-05005RealPartx104E£d<%ewIMeftJoo½DesktopWndOWbdpaa-iQ、.、门壮/s"三三x104NdGs?E-8pJneChebyshev1：clearall;wp=2000*2*pi;ws=10000*2*pi;Fs=44100;Wp=wpFs;Ws=wsFs;Ap=O.5;As=50;N=Cheblord(wpzws,Ap,As,s,);fprintf(,N=%.Ofn,N)wc=wp(10(0.1*Ap)-1)(1N2);numazdena=chebyl(N,Apzwc,'s,);numd,dend=bilinear(numazdena,Fs)；W=Iinspace(O,pi,2048);h=freqz(numd,dend,w);norm=max(abs（三）);figure(1);zplane(numazdena);figure(2);plot(wpiz20*logl0(abs(hnorm);xlabel(,Normalizedfrequency,);ylabel(,Gain,dB,);w=WpWs;h=freqz(numdzdend,w);fprintf('Ap=%.4fn',-20*IoglO(abs(h(l);fprintf('As=%.4fn,-20*IoglO(abs(h(2);gridon;numd=numdnorm;11Figure225-2-15-1-05005RealPartHU11.O!匕t¾lIfaEditywMftTookk½>pBndoWtilpjBesaQc电要/aIeI日Ggx10451505151.o0.1UodP£?£-35002040506070809HOfmSkZedequncy氏EditYieWInsertlookRedCtOP如ndowH*。d，Q、器*/0盟Chcbyshev2：clearall;wp=2000*2*pi;ws=10000*2*pi;Fs=44100;Wp=wpFs;Ws=wsFs;Ap=O.5;As=50;N=cheb2ord(wp,ws,Ap,As,s,);fprintf(,N=%.0fn,rN)wc=wp(10(0.1*Ap)-1)(1N2);numazdena=cheby2(N,As,wc,'s');numdzdend=bilinear(numa,dena,Fs)；W=Iinspace(0zpi,2048);h=freqz(numdzdend,w);norm=max(abs（三）);numd=numdnorm;figure(1);zplane(numazdena);figure(2);plot(wpi,20*lol0(abs(hnorm);xlabel(,Normalizedfrequency,);ylabel(,Gain,dB,);w=WpWs;h=freqz(numdzdend,w);fprintf('Ap=%.4fn',-2O*IoglO(abs(h(l);fprintf(,As=%.4fn,-2O*IoglO(abs(h(2);gridon;ReaiPartFurelIOlI曲EdtywEr100QtktopW>ndowMP*a、osXva0XlO4椭圆：clearall;wp=2000*2*pi;ws=10000*2*pi;Fs=44100;Wp=wpFs;Ws=wsFs;Ap=O.5;As=50;N=ellipord(wp,ws,ApzAs,s,);fprintf(,N=%.Ofn,N)wc=wp(10(0.1*Ap)-1)(1N2);numazdena=ellip(N,Ap,As,wc,s'),numd,dend=bilinear(numazdena,Fs)；W=Iinspace(O,pi,2048);h=freqz(numd,dend,w);norm=max(abs（三）);numd=numdnorm;figure(1);zplane(numazdena);figure(2);plot(wpiz20*logl0(abs(hnorm);xlabel(,Normalizedfrequency,);ylabel(,Gain,dB,);w=WpWs;h=freqz(numdzdend,w);fprintf('Ap=%.4fn',-2O*IoglO(abs(h(l);fprintf('As=%.4fn',-2O*IoglO(abs(h(2);gridon;S-F*y*IfQMfcWOi，njyQ3>z匕【研讨题目】基本题2 .窗函数探讨分析矩形窗、汉纳窗、哈明窗、布莱克曼窗、凯泽窗的频域特性，并进行比较。利用I型线性相位滤波器设计满意下列指标的FIR高通滤波器p=0.811,s=0.711,Ap=O.3dBAs=40dB【结果分析】(1) AP=OdBASQ20dB(2) APKO.034dBASF44dB(3) APQOdBASQ55dB(4) APQOdBASF8dB(5) APQO.057dBASQ42dB各种窗的比较矩形窗，10kM()其他图为矩形窗设计的FIR滤波器在不连续点旁边的幅度函数A()
