iir.m

用双线性变换法设计IIR数字滤波器 （1）用双线性变换法设计一个巴特沃斯低通IIR 数字滤波器。设计指标参数为：在通 带内频率低于0.2π 时

clear all;
A=[0.09036,0.09036*2,0.09036];
B1=[1,-1.2686,0.7051];
B2=[1,-1.0106,0.3583];
B3=[1,-0.9044,0.2155];
[H1,w]=freqz(A,B1,50);
[H2,w]=freqz(A,B2,50);
[H3,w]=freqz(A,B3,50);
h=H1.*H2;
H=h.*H3;
i=1:50;
a=20*log10(abs(H(i))+eps/abs(H(1)));
b=20*log10(abs(H1(i))+eps/abs(H1(1)));
c=20*log10(abs(H2(i))+eps/abs(H2(1)));
d=20*log10(abs(H3(i))+eps/abs(H3(1)));

figure(1);
subplot(2,2,1);
plot(w/pi,a);
axis([0,0.5,-50,10]);
title('滤波器的幅频响应特性曲线');
xlabel('w/\pi');ylabel('20lg|H(ej0)/H(ejw)|');
grid on;

subplot(2,2,2);
plot(w/pi,b);
axis([0,0.5,-50,10]);
title('第一级二阶滤波器幅频响应特性曲线');
xlabel('w/\pi');ylabel('20lg|H1(ej0)/H1(ejw)|');
grid on;

subplot(2,2,3);
plot(w/pi,b);
axis([0,0.5,-50,10]);
title('第二级二阶滤波器幅频响应特性曲线');
xlabel('w/\pi');ylabel('20lg|H2(ej0)/H2(ejw)|');
grid on;

subplot(2,2,4);
plot(w/pi,b);
axis([0,0.5,-50,10]);
title('第三级二阶滤波器幅频响应特性曲线');
xlabel('w/\pi');ylabel('20lg|H3(ej0)/H3(ejw)|');
grid on;

x=[-4,-2,0,-4,-6,-4,-2,-4,-6,-6,-4,-4,-6,-6,-2,6,12,8,0,-16,-38,-60,-84,-90,-66,-32,-4,-2,-4,8,12,12,10,6,6,6,4,0,0,0,0,0,-2,-4,0,0,0,-2,-2,0,0,-2,-2,-2,-2,0];
j=0:55;
figure(2);
subplot(2,2,1);
stem(j,x,'.');
title('心电图信号采样序列');
xlabel('n');ylabel('x(n)');

y1=filter(A,B1,x);
subplot(2,2,2);
stem(j,y1,'.');
title('通过一级滤波后的心电图信号');
xlabel('n');ylabel('y1(n)');

y2=filter(A,B2,y1);
subplot(2,2,3);
stem(j,y2,'.');
title('通过二级滤波后的心电图信号');
xlabel('n');ylabel('y2(n)');

y3=filter(A,B3,y2);
subplot(2,2,4);
stem(j,y3,'.');
title('通过三级滤波后的心电图信号');
xlabel('n');ylabel('y3(n)');