实验七-华北电力大学-数字信号处理实验

1、实 验 报 告实验名称_ _课程名称_ _院 系 部: 专业班级：学生姓名： 学 号:同 组 人: 实验台号:指导教师： 成 绩： 实验日期:华北电力大学1. 实验目的加深理解IIR数字滤波器的特性，掌握IIR数字滤波器的设计原理与设计方法，以及IIR数字滤波器的应用。2. 实验原理3. 实验内容及步骤4. 数据处理与总结1.(1)clear;fsam=100;t0=1/fsam;t=6;k=0:t0:t;N=512; x=1+cos(pi/4.*k/t0)+cos(2*pi/3.*k/t0); f=(-N/2:(N/2-1)/N*2*pi; N1,Wc=buttord(1/4,1/2,3,6

2、0);b,a=butter(N1,Wc,'low'); freqz(b,a); figure;axis(0,1,-120,0);y=filter(b,a,x);Y=fftshift(fft(y,N);stem(f,abs(Y); 右图一为数字低通滤波器的幅频响应和相频响应。右图二为信号经过滤波器后输出信号的频谱。(2)clear;fsam=100;t0=1/fsam;t=6;k=0:t0:t;N=512; x=1+cos(pi/4.*k/t0)+cos(2*pi/3.*k/t0); f=(-N/2:(N/2-1)/N*2*pi; N1,Wc=buttord(2/3,10/24,

3、3,100);b,a=butter(N1,Wc,'high'); freqz(b,a); figure;axis(0,1,-120,0);y=filter(b,a,x); Y=fftshift(fft(y,N);stem(f,abs(Y);右图一为数字高通滤波器的幅频响应和相频响应。右图二为信号经过滤波器后输出信号的频谱。(3)clear;fsam=100;t0=1/fsam;t=6;k=0:t0:t;N=512; x=1+cos(pi/4.*k/t0)+cos(2*pi/3.*k/t0); f=(-N/2:(N/2-1)/N*2*pi; N1,Wc=buttord(1/8 8

4、/24,1/32 2/3,3,60);b,a=butter(N1,Wc,'bandpass'); freqz(b,a); figure;axis(0,1,-120,0);y=filter(b,a,x);Y=fftshift(fft(y,N);stem(f,abs(Y); 右图一为数字带通滤波器的幅频响应和相频响应。右图二为信号经过滤波器后输出信号的频谱。(4)clear;fsam=100;t0=1/fsam;t=6;k=0:t0:t;N=512; x=1+cos(pi/4.*k/t0)+cos(2*pi/3.*k/t0); f=(-N/2:(N/2-1)/N*2*pi; N1,

5、Wc=buttord(1/32 2/3,0.2 10/27,3,60);b,a=butter(N1,Wc,'stop'); freqz(b,a); figure;axis(0,1,-120,0);y=filter(b,a,x);Y=fftshift(fft(y,N);stem(f,abs(Y);右图一为数字带阻滤波器的幅频响应和相频响应。右图二为信号经过滤波器后输出信号的频谱。2.(1).脉冲响应不变法clear;omegas=0.2 0.72*pi;omegap=0.3 0.6*pi;Ap=1;As=42; Fs=1;ws=omegas*Fs;wp=omegap*Fs;N,W

6、c=buttord(wp,ws,Ap,As,'s');b,a=butter(N,Wc,'bandpass','s'); % N,Wc=cheb1ord(wp,ws,Ap,As,'s');% b,a=cheby1(N,Ap,Wc,'bandpass','s');% N,Wc=cheb2ord(wp,ws,Ap,As,'s');% b,a=cheby2(N,As,Wc,'bandpass','s');% % N,Wc=ellipord(wp,ws,Ap,A

7、s,'s');% b,a=ellip(N,Ap,As,Wc,'bandpass','s');numd,dend=impinvar(b,a,Fs);w=linspace(0,pi,512); h=freqz(numd,dend,w);norm=max(abs(h);numd=numd/norm;plot(w/pi,20*log10(abs(h)/norm);grid on右图从上到下分别是buttordCheby1 cheby2 ellipord 型滤波器的频率特性(脉冲响应不变法)(2)双线性变换法clear;omegas=0.2 0.72*pi

8、; omegap=0.3 0.6*pi;Ap=1;As=42;Fs=1;T=1/Fs;wp=2*tan(omegap/2)/T;ws=2*tan(omegas/2)/T;% N,Wc=buttord(wp,ws,Ap,As,'s');% b,a=butter(N,Wc,'bandpass','s');% N,Wc=cheb1ord(wp,ws,Ap,As,'s'); % b,a=cheby1(N,Ap,Wc,'bandpass','s');% % N,Wc=cheb2ord(wp,ws,Ap,As,

9、's');% b,a=cheby2(N,As,Wc,'bandpass','s');N,Wc=ellipord(wp,ws,Ap,As,'s');b,a=ellip(N,Ap,As,Wc,'bandpass','s');numd,dend=bilinear(b,a,Fs);w=linspace(0,pi,512); h=freqz(numd,dend,w);norm=max(abs(h);numd=numd/norm;plot(w/pi,20*log10(abs(h)/norm);grid onti

10、tle('ellipord')右图从上到下分别是buttordCheby1 cheby2 ellipord 型滤波器的频率特性(双线性变换法)3.(1)clear;k=0:204;N=205;x=sin(2*pi*770/8000.*k)+sin(2*pi*1209/8000.*k);stem(k,x);title('时域波形')figure;X=fftshift(fft(x);omega=(-(N-1)/2):(N-1)/2)/N*2*pi;stem(omega,abs(X);title('频谱图')(2)clear;k=0:204;N=205

11、;x=sin(2*pi*770/8000.*k)+sin(2*pi*1209/8000.*k);omega=(-(N-1)/2):(N-1)/2)/N*2*pi;%低通wp=2*941/8000;ws=2*1200/8000;Ap=3;As=60;N,wc=buttord(wp,ws,Ap,As);b,a=butter(N,wc);freqz(b,a);figure%滤波输出y=filter(b,a,x);Y=fftshift(fft(y);stem(omega,abs(Y)clear;k=0:204;N=205;x=sin(2*pi*770/8000.*k)+sin(2*pi*1209/80

12、00.*k);omega=(-(N-1)/2):(N-1)/2)/N*2*pi;%高通wp=2*1200/8000;ws=2*1000/8000;Ap=3;As=60;N,wc=buttord(wp,ws,Ap,As);b,a=butter(N,wc,'high');freqz(b,a);figure%滤波输出y=filter(b,a,x);Y=fftshift(fft(y);stem(omega,abs(Y)(3)clear;k=0:204;N=205;x=sin(2*pi*770/8000.*k)+sin(2*pi*1209/8000.*k);omega=(-(N-1)/2

13、):(N-1)/2)/N*2*pi;wp1=692 702./4000;ws1=687 707./4000;wp2=765 775./4000;ws2=760 780./4000;wp3=847 857./4000;ws3=842 862./4000;wp4=936 946./4000;ws4=931 951./4000;Ap=3;As=30;N1,wc1=buttord(wp1,ws1,Ap,As);b1,a1=butter(N1,wc1,'bandpass');N2,wc2=buttord(wp2,ws2,Ap,As);b2,a2=butter(N2,wc2,'ba

14、ndpass');N3,wc3=buttord(wp3,ws3,Ap,As);b3,a3=butter(N3,wc3,'bandpass');N4,wc4=buttord(wp4,ws4,Ap,As);b4,a4=butter(N4,wc4,'bandpass');figure(1)freqz(b1,a1);figure(2)freqz(b2,a2);figure(3)freqz(b3,a3);figure(4)freqz(b4,a4);以上分别是4个带通滤波器的幅频响应.clear;k=0:204;N=205;x=sin(2*pi*770/8000.*

15、k)+sin(2*pi*1209/8000.*k);omega=(-(N-1)/2):(N-1)/2)/N*2*pi;wp1=692 702./4000;ws1=687 707./4000;wp2=765 775./4000;ws2=760 780./4000;wp3=847 857./4000;ws3=842 862./4000;wp4=936 946./4000;ws4=931 951./4000;Ap=3;As=20;N1,wc1=buttord(wp1,ws1,Ap,As);b1,a1=butter(N1,wc1,'bandpass');N2,wc2=buttord(w

16、p2,ws2,Ap,As);b2,a2=butter(N2,wc2,'bandpass');N3,wc3=buttord(wp3,ws3,Ap,As);b3,a3=butter(N3,wc3,'bandpass');N4,wc4=buttord(wp4,ws4,Ap,As);b4,a4=butter(N4,wc4,'bandpass');y1=filter(b1,a1,x);Y1=abs(fftshift(fft(y1);y2=filter(b2,a2,x);Y2=abs(fftshift(fft(y2);y3=filter(b3,a3,x);Y

17、3=abs(fftshift(fft(y3);y4=filter(b4,a4,x);Y4=abs(fftshift(fft(y4);plot(omega,Y1,'-g',omega,Y2,'-r',omega,Y3,'-b',omega,Y4,'-k');由图中可以看出bp770hz滤波器的输出最大，所以该dtmf的行频为770hz（4）clear;k=0:204;N=205;x=sin(2*pi*770/8000.*k)+sin(2*pi*1209/8000.*k);omega=(-(N-1)/2):(N-1)/2)/N*2*p

18、i;wp1=1204 1214./4000;ws1=1199 1219./4000;wp2=1331 1341./4000;ws2=1326 1346./4000;wp3=1472 1482./4000;ws3=1467 1487./4000;Ap=3;As=20;N1,wc1=buttord(wp1,ws1,Ap,As);b1,a1=butter(N1,wc1,'bandpass');N2,wc2=buttord(wp2,ws2,Ap,As);b2,a2=butter(N2,wc2,'bandpass');N3,wc3=buttord(wp3,ws3,Ap,A

19、s);b3,a3=butter(N3,wc3,'bandpass');y1=filter(b1,a1,x);Y1=abs(fftshift(fft(y1);y2=filter(b2,a2,x);Y2=abs(fftshift(fft(y2);y3=filter(b3,a3,x);Y3=abs(fftshift(fft(y3);plot(omega,Y1,'-g',omega,Y2,'-r',omega,Y3,'-b');图中可以看出bp1209hz滤波器输出最大由(3)(4)可以得出dtmf信号按键为4(5)x=sin(2*pi*770/8000.*k)+sin(2*pi*1477/8000.*k);检验数字6行频输出列频输出得dtmf信号按键为6(6)答:可以,只要取的各个频率的表示颜色不同即可.5.实验思考题1. 哪些主要因素直接影响IIR数字滤波器的阶数？从工程概念进行定性解释。答：通带截频，阻带截频，通带最大衰减和阻带最大衰减。2. 巴特沃斯、切比雪夫I 型、切比雪夫II 型和椭圆模拟原型滤波器的幅频特性有哪些特点？其优缺点是什么？答：巴特沃斯滤波器的特点是通频带内的频率响应曲线最大限度平坦，没有起伏，而在阻频带则逐渐下降为零。 在振幅的对数对角频率的波特图上,从某一边界