实验一 连续时间系统的时域和频域分析

脉冲响应不变法：
wp=0.2*pi;ws=0.3*pi;
rp=1;rs=15;
fs=1;
omegap=wp*fs;omegas=ws*fs;
[N,Wn]=buttord(omegap,omegas,rp,rs,'s');
[b,a]=butter(N,Wn,'s');
[h,omega]=freqs(b,a);
fp1=10;wp1=2*pi*fp1;
fp2=25;wp2=2*pi*fp2;
omegap=[wp1 wp2];
fs1=5;ws1=2*pi*fs1;
fs2=30;ws2=2*pi*fs2;
omegas=[ws1 ws2];
bw=wp2-wp1;w0=sqrt(ws1*ws2);
rp=3;rs=30;
rp=1;rs=15;
fs=1; T=1/fs;
omegap=(2/T)*tan(wp/2);omegas=(2/T)*tan(ws/2);
[N,Wn]=buttord(omegap,omegas,rp,rs,'s');
[b,a]=butter(N,Wn,'s');
[h,omega]=freqs(b,a);
axis([0 5 -100 10]);
title('模拟滤波器的幅频响应');ylabel('dB');
subplot(122)
plot(w/pi,dbh1);grid
axis([0 2 -80 10]);
title('数字滤波器的幅频响应');ylabel('dB');
2.用脉冲响应不变法设计一个数字低通滤波器，使其特征逼近一个低通Butterworth模拟滤波器的下列性能指标：通带截止频率 ，通带最大衰减 ，阻带截止频率 ，阻带最小衰减 ，设采样频率 。假设该数字低通滤波器有一个输入信号 ，其中， ， 。试将滤波器的输出信号与输入信号进行比较。
ylabel('dB');
subplot(222),plot(omega0/(2*pi),angle(H));grid
axis([0,1,-4,4]);title('归一化模拟低通原型相位响应');
ylabel('弧度');
subplot(223),plot(omega1/(2*pi),dbH1);grid
axis([0,1,-50,1]);title('归一化模拟低通原型幅度响应');
ylabel('dB');
subplot(222),plot(omega0/(2*pi),angle(H));grid
axis([0,1,-4,4]);title('归一化模拟低通原型相位响应');
ylabel('弧度');
dbh=20*log10(abs(h)/max(abs(h)));
[bz1,az1]=impinvar(b,a,fs);
[h1,w]=freqz(bz1,az1,256,'whole');
dbh1=20*log10(abs(h1)/max(abs(h1)));
subplot(121)
plot(omega,dbh);grid
fp=5;
wp=2*pi*fp;
fs=12;
ws=2*pi*fs;
rp=2;
rs=30;
[N,Wn]=buttord(wp,ws,rp,rs,'s');
[b,a]=butter(N,Wn,'s');
freqs(b,a)
2.设计一个巴特沃斯模拟高通滤波器，以满足：通带截止频率 ，通带最大衰减 ，阻带截止频率 ，阻带最小衰减 。要求绘出滤波器的幅频特性曲线。（幅度用分贝值表示）
dbh=20*log10(abs(h)/max(abs(h)));
[bz1,az1]=bilinear(b,a,fs);
[h1,w]=freqz(bz1,az1,256,'whole');
dbh1=20*log10(abs(h1)/max(abs(h1)));
subplot(121)
plot(omega,dbh);grid
ylabel('弧度');xlabel('频率(HZ)');
4.设计一个巴特沃斯模拟带阻滤波器，以满足：通带截止频率分别为10HZ、35HZ，阻带截止频率分别为15HZ、30HZ，通带最大衰减为3dB，阻带最小衰减为30dB。要求绘出滤波器的幅频特性曲线。（幅度用分贝值表示）
fp1=10;wp1=2*pi*fp1;
[z0,p0,k0]=buttap(N);
b0=k0*real(poly(z0));
a0=real(poly(p0));
[H,omega0]=freqs(b0,a0);
dbH=20*log10((abs(H)+eps)/max(abs(H)));
[b1,a1]=lp2bs(b0,a0,w0,bw);
axis([0,40,-50,1]);title('实际模拟带通幅度响应');
ylabel('dB');xlabel('频率(HZ)');
subplot(224),plot(omega1/(2*pi),angle(H1));grid
axis([0,40,-4,4]);title('实际模拟带通相位响应');
ylabel('dB');xlabel('频率(HZ)');
subplot(224),plot(omega1/(2*pi),angle(H1));grid
axis([0,40,-4,4]);title('实际模拟带通相位响应');
ylabel('弧度');xlabel('频率(HZ)');
1.要求分别用脉冲响应不变法和双线性变换法设计一个数字低通滤波器，以满足：通带截止频率为 ，阻带截止频率为 ，通带最大衰减为1dB，阻带最小衰减为15dB，采样间隔设为1s。
[bz,az]=impinvar(B,A,10000);
figure(1);
freqz(bz,az,w);
title('用脉冲响应不变法设计的数字低通滤波器');
shg;
figure(2);
y=filter(bz,az,x);
subplot(121);
plot(t,x);
grid on;
title('输入信号');
fp=20;
wp=2*pi*fp;
fs=10;
ws=2*pi*fs;
rp=3;
rs=15;
[N,omegac]=buttord(wp,ws,rp,rs,'s');
[z0,p0,k0]=buttap(N);
b0=k0*real(poly(z0));
a0=real(poly(p0));
[H,omega0]=freqs(b0,a0);
[N,omegac]=buttord(omegap,omegas,rp,rs,'s');
[z0,p0,k0]=buttap(N);
b0=k0*real(poly(z0));
a0=real(poly(p0));
[H,omega0]=freqs(b0,a0);
dbH=20*log10((abs(H)+eps)/max(abs(H)));
dbH=20*log10((abs(H)+eps)/max(abs(H)));
[b1,a1]=lp2hp(b0,a0,omegac);
[H1,omega1]=freqs(b1,a1);
dbH1=20*log10((abs(H1)+eps)/max(abs(H1)));
subplot(221),plot(omega0/(2*pi),dbH);grid
axis([0,2*fs,-4,4]);title('实际模拟高通相位响应');
ylabel('弧度');xlabel('频率(HZ)');
3.设计一个巴特沃斯模拟带通滤波器，以满足：通带范围为10Hz～25Hz，阻带截止频率分别为5Hz、30Hz，通带最大衰减为3dB，阻带最小衰减为30dB。要求绘出滤波器的幅频特性曲线。（幅度用分贝值表示）
subplot(223),plot(omega1/(2*pi),dbH1);grid
axis([0,2*fs,-50,label('dB');xlabel('频率(HZ)');
subplot(224),plot(omega1/(2*pi),angle(H1));grid
fp2=35;wp2=2*pi*fp2;
omegap=[wp1 wp2];
fs1=15;ws1=2*pi*fs1;
fs2=30;ws2=2*pi*fs2;
omegas=[ws1 ws2];
bw=wp2-wp1;w0=sqrt(ws1*ws2);
rp=3;rs=30;
[N,omegac]=buttord(omegap,omegas,rp,rs,'s');
subplot(222),plot(omega0/(2*pi),angle(H));grid
axis([0,1,-4,4]);title('归一化模拟低通原型相位响应');
ylabel('弧度');
subplot(223),plot(omega1/(2*pi),dbH1);grid