DSP研究性学习报告滤波器设计

《数字信号处理》课程争论性学习报告数字滤波器设计专题研讨【目的】把握IIR和FIR数字滤波器的设计方法及各自的特点。把握各种窗函数的时频特性及对滤波器设计的影响。培育学生自主学习力气，以及觉察问题、分析问题和解决问题的力气。【1】44.1kHz)f=2kHz， f=10kHz, A=0.5dB,A=50dBp s p s分别用双线性变换和冲激响应不变法设计一个BWIChebyshevII并进展比较。【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。但假设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〔T〕将对设计结果有影响。【设计步骤】变换为相应的数字滤波器数字滤波器设计【数字滤波器设计【果分析】模拟滤波器设计指标【仿真结果】双线性不变法Ap=0.2445As=50.00000-50-100值-150幅-200-250-3000 0.1 0.2 0.3 0.4 0.5Ω／π

0.6 0.7 0.8 0.9 1模拟低通滤波器模拟低通滤波器〕数字低通滤波器〕双线性法冲击不变法Ap=0.4618As=60.40500-10-20-30-40值-50幅-60-70-80-90-1000 0.1 0.2 0.3 0.4 0.5Ω／π

0.6 0.7 0.8 0.9 1ChebyshevI型Ap=0.4999As=71.05630-100值-200幅-300-4000 0.1 0.2 0.3 0.4 0.5Ω／π

0.6 0.7 0.8 0.9 1PmI

10.50-0.5-1

-3 -2 -1 0RealPart

1 2 3Ap=0.5000As=53.05770值-50幅-1000 0.1 0.2 0.3 0.4 0.5Ω／π

0.6 0.7 0.8 0.9 1PmI

10.50-0.5-1

-3 -2 -1 0RealPart

1 2 3椭圆型滤波器Ap=0.5000As=51.23550-100值-200幅-300-4000 0.1 0.2 0.3 0.4 0.5Ω／π

0.6 0.7 0.8 0.9 1PmI

10.50-0.5-1

-3 -2 -1 0RealPart

1 2 3【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。ChebyshevIChebyshevII性的。ChebyshevIChebyshevII阶数相等，它们的裕量也不同。零极点分布都是关于虚轴对称且都在单位圆内。总体来看，BW【自主学习内容】利用matlab实现脉冲响应不变法和双线性变换法的程序语言【阅读文献】《数字信号处理》陈后金【问题探究】BWChebyshevIChebyshevII双线性变换法的优缺点优点：不会产生频谱混叠脉冲响应不变法的优缺点优点：数字滤波器和模拟滤波器的频率关系为线性缺点：存在频谱混叠，不能用脉冲响应不变法设计高通、带阻等滤波器。型、Chebyshev I型、Chebyshev I I型和椭圆型滤波器的特点;即使阶数相等，它们的裕量也不同。在滤波器的实现过程中，〔H(s)的极点离jw。Cheby2ws【仿真程序】双线性变换法>>clear;>>FS=44100;fp=2023;fs=10000;>>Ap=0.5;As=50;>> wp=fp*2*pi; ws=fs*2*pi;wp1=wp/FS;ws1=ws/FS;>>OmegaP=2*FS*tan(wp1/2);>>OmegaS=2*FS*tan(ws1/2);>>[N,wc]=buttord(OmegaP,OmegaS,Ap,As,”s”);>>[bt,at]=butter(N,wc,”s”);>>[bz,az]=bilinear(bt,at,FS);Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=1.e-024.Inbilinearat89Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=1.e-024.Inbilinearat90>>w=linspace(0,pi,512);h=freqz(bz,az,w); norm=max(abs(h));>>bz=bz/norm;>>plot((w/pi),20*log10(abs(h)/norm));>> xlabel(”Ω／π”);ylabel(”幅值”);>>w=[wp1ws1];h=freqz(bz,az,w);>>fprintf(”Ap=%.4f\n”,-20*log10(abs(h(1))));Ap=0.2445>>fprintf(”As=%.4f\n”,-20*log10(abs(h(2))));As=50.0000>>gridon;脉冲响应不变法>>clear;>>FS=44100;>>fp=2023;fs=10000;>>ws=fs*2*pi;>>wp=fp*2*pi;>>Ws=ws/FS;Wp=wp/FS;>>Ap=0.5;As=50;>>N=buttord(wp,ws,Ap,As,”s”);>>fprintf(”N=%.0f\n”,N);N=10>>wc=wp/10^(0.1*Ap-1)^(1/N/2);>>[n,d]=butter(N,wc,”s”);correct/robust.CoeffsofB(s)/A(s)arereal,butB(z)/A(z)hascomplexcoeffs.Probablecauseisrootingofhigh-orderrepeatedpolesinA(s).Inimpinvarat122>>w=linspace(0,pi,512);>>h=freqz(n,d,w);>>norm=max(abs(h));>>n=n/norm;>>plot(w/pi,20*log10(abs(h)/norm));xlabel(”Ω／π”);ylabel(”幅值”);>>w=[WpWs];>>h=freqz(n,d,w);>>fprintf(”Ap=%.4f\n”,-20*log10(abs(h(1))));fprintf(”As=%.4f\n”,-20*log10(abs(h(2))));Ap=0.4618As=60.4050>>gridon;ChebyshevI>>clear;>>FS=44100;>>fp=20230;fs=10000;>>Ap=0.5;As=50;>>wp=fp*2*pi;>>ws=fs*2*pi;>>wp1=wp/FS;>>ws1=ws/FS;>>OmegaP=2*FS*tan(wp1/2);>>OmegaP=2*FS*tan(ws1/2);>>[N,wc]=cheb1ord(OmegaP,OmegaS,Ap,As,”s”);>>[bt,at]=cheby1(N,Ap,wc,”s”);>>[bz,az]=bilinear(bt,at,FS);>>w=linspace(0,pi,512);Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=9.e-023.Inbilinearat89Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=9.e-023.Inbilinearat90z>>h=freqz(bz,az,w);>>norm=max(abs(h));>>bz=bz/norm;subplot(2,1,1);>>plot((w/pi),20*log10(abs(h)/norm));>>xlabel(”Ω／π”);ylabel(”幅值”);>>[r,p,k]=residuez(bz,az);>>subplot(2,1,2);>>zplane(bz,az);>>w=[wp1ws1];>>h=freqz(bz,az,w);>>fprintf(”Ap=%.4f\n”,-20*log10(abs(h(1))));Ap=0.4999>>fprintf(”As=%.4f\n”,-20*log10(abs(h(2))));As=71.0563ChebyshevII>>clear;>>FS=44100;>>fp=20230;fs=10000;>>Ap=0.5;As=50;>>wp=fp*2*pi;>>ws=fs*2*pi;>>wp1=wp/FS;>>ws1=ws/FS;>>OmegaP=2*FS*tan(wp1/2);>>OmegaP=2*FS*tan(ws1/2);>>[N,wc]=cheb2ord(OmegaP,OmegaS,Ap,As,”s”);>>[bt,at]=cheby2(N,As,wc,”s”);>>[bz,az]=bilinear(bt,at,FS);Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=1.e-024.Inbilinearat89Warning:Matrixisclosetosingularorbadlyscaled.Resultsmaybeinaccurate.RCOND=1.e-024.Inbilinearat90>>w=linspace(0,pi,512);>>h=freqz(bz,az,w);>>norm=max(abs(h));>>bz=bz/norm;>>subplot(2,1,1);>>plot((w/pi),20*log10(abs(h)/norm));xlabel(”Ω／π”);ylabel(”幅值”);>>[r,p,k]=residuez(bz,az);>>subplot(2,1,2);>>zplane(bz,az);>>w=[wp1ws1];>>h=freqz(bz,az,w);>> fprintf(”Ap= %.4f\n”,-20*log10(abs(h(1))));fprintf(”As=%.4f\n”,-20*log10(abs(h(2))));Ap=0.5000As=53.0577椭圆型滤波器>>clear;>>FS=44100;>>fp=20230;fs=10000;>>Ap=0.5;As=50;>>wp=fp*2*pi;>>ws=fs*2*pi;>>wp1=wp/FS;>>ws1=ws/FS;>>OmegaP=2*FS*tan(wp1/2);>>OmegaP=2*FS*tan(ws1/2);>>[N,wc]=ellipord(OmegaP,OmegaS,Ap,As,”s”);>>[bt,at]=ellip(N,Ap,As,wc,”s”);>>[bz,az]=bilinear(bt,at,FS);>>w=linspace(0,pi,512);>>h=freqz(bz,az,w);>>norm=max(abs(h));>>bz=bz/norm;>>subplot(2,1,1);>>plot((w/pi),20*log10(abs(h)/norm));xlabel(”Ω／π”);ylabel(”幅值”);>>[r,p,k]=residuez(bz,az);>>subplot(2,1,2);zplane(bz,az);>>w=[wp1ws1];>>h=freqz(bz,az,w);>>fprintf(”Ap=%.4f\n”,-20*log10(abs(h(1)))); >>fprintf(”As=%.4f\n”,-20*log10(abs(h(2))));Ap=0.5000As=51.2355【研讨题目2】FIR【温馨提示】H(ejIDTFTdd dej(H(ej)。d

0.5M 参与理常用窗函数除矩形窗外，还有Hann(汉纳)窗、Hamming(哈明)窗、Blackman(布莱克〔主瓣宽度、旁瓣幅度〕不同，使得所设计的滤波器过渡带宽度和阻带衰减也不同。【设计步骤】Wp=0.67π,Ws=0.53π,Ap=0.3dB,As=50dB承受矩形窗加窗截断blackman承受hanning窗加窗截断承受凯泽窗加窗截断【仿真结果】N=51承受矩形窗加窗截断Ap≈0dB As≈21dB100-10-20-30-40-50-60-70-80-900 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1承受Hamming窗加窗截断Ap≈0dB As≈54dB200-20-40-60-80-100-120

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1承受blackman窗加窗截断Ap≈0dB As≈75dB200-20-40-60-80-100-120-1400 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1承受hanning窗加窗截断Ap≈0dB 200-20-40-60-80-100-120-1400 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1承受凯泽窗加窗截断Ap≈0dB 200-20-40-60-80-100-120-1400 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1【结果分析】窗的类型主瓣宽度近似过度宽窗的类型主瓣宽度近似过度宽ApAs度p s矩形4/L1.8/L0.090.8221Hann8/L6.2/L0.00640.05644Hamming8/L7/L0.00220.01953Blackman12/L11.4/L0.00020.001774【自主学习内容】W=hanning〔N)W=hamming〔N)W=blackman〔N)W=baiser〔N〕其中Nw是一个长度为NN点的取值。【阅读文献】《数字信号处理》陈后金【问题探究】矩形窗的过渡带最窄，但设计出的FIR二者进展折中权衡处理。【仿真程序】矩形窗>>Wp=0.67*pi;Ws=0.53*pi;Ap=0.3;As=50;>>N=ceil(7*pi/(Wp-Ws));>>N=mod(N+1,2)+N;>>M=N-1;>>fprintf(”N=%.0f\n”,N);N=51>>w=boxcar(N)”;Wc=(Wp+Ws)/2;>>k=0:M;>>hd=-(Wc/pi)*sinc(Wc*(k-0.5*M)/pi);>>hd(0.5*M+1)=hd(0.5*M+1)+1;>>h=hd.*w; omega=linspace(0,pi,512);>>mag=freqz(h,[1],omega);magdb=20*log10(abs(mag));>>plot(omega/pi,magdb);哈明窗：>>Wp=0.67*pi;Ws=0.53*pi;Ap=0.3;As=50;>>N=ceil(7*pi/(Wp-Ws));>>N=mod(N+1,2)+N;>>M=N-1;fprintf(”N=%.0f\n”,N);N=51>>w=hamming(N)”;Wc=(Wp+Ws)/2;>>k=0:M; hd=-(Wc/pi)*sinc(Wc*(k-0.5*M)/pi);>>hd(0.5*M+1)=hd(0.5*M+1)+1;h=hd.*w;omega=linspace(0,pi,512);>>mag=freqz(h,[1],omega);magdb=20*log10(abs(mag)); plot(omega/pi,magdb)布莱克曼窗>>Wp=0.67*pi;Ws=0.53*pi;Ap=0.3;As=50;>>N=ceil(7*pi/(Wp-Ws));N=mod(N+1,2)+N;>>M=N-1;>>fprintf(”N=%.0f\n”,N);N=51>>w=blackman(N)”;Wc=(Wp+Ws)/2;>>k=0:M;>>hd=-(Wc/pi)*sinc(