零点分布对单位脉冲响应的影响

共四个二阶网络的系统函数，画系统零极点分布图，求各系统单位脉冲响应，画波形

H1

 clc;
 clear all;
 close all;
 A=[1,-1.6,0.9425];
 B=[1,0,0];
 figure
 zplane(B,A);
 z=roots(B) %zero-point
 p=roots(A) %polar-point
 pm=abs(p);
 if max(pm)<1
     disp('system is stable and causal'),
 else
     disp('system is not stable and causal'),
 end
 [h1n,n]=impz(B,A,100);
 figure
 stem(n,h1n,'.');
 line([0,100],[0,0])
 xlabel('n');
 ylabel('h1n');

零点在原点，零点不影响系统频率特性，零点不影响单位脉冲响应

H2

 clc;
 clear all;
 close all;
 A=[1,-1.6,0.9425];
 B=[1,-0.3,0];
 figure
 zplane(B,A);
 z=roots(B) %zero-point
 p=roots(A) %polar-point
 pm=abs(p);
 if max(pm)<1
     disp('system is stable and causal'),
 else
     disp('system is not stable and causal'),
 end
 [h1n,n]=impz(B,A,100); 
 figure
 stem(n,h1n,'.');
 xlabel('n');
 ylabel('h1n');
 axis([0 100 -2 2]);

零点离极点比较远

H3

 clc;
 clear all;
 close all;
 A=[1,-1.6,0.9425];
 B=[1,-0.8,0];
 figure
 zplane(B,A);
 z=roots(B) %zero-point
 p=roots(A) %polar-point
 pm=abs(p);
 if max(pm)<1
     disp('system is stable and causal'),
 else
     disp('system is not stable and causal'),
 end
 [h1n,n]=impz(B,A,100); 
 figure
 stem(n,h1n,'.');
 xlabel('n');
 ylabel('h1n');
 axis([0 100 -2 2]);

H4

 clc;
 clear all;
 close all;
 A=[1,-1.6,0.9425];
 B=[1,-1.6,0.8];
 figure
 zplane(B,A);
 z=roots(B) %zero-point
 p=roots(A) %polar-point
 pm=abs(p);
 if max(pm)<1
     disp('system is stable and causal'),
 else
     disp('system is not stable and causal'),
 end
 [h1n,n]=impz(B,A,100); 
 figure
 stem(n,h1n,'.');
 xlabel('n');
 ylabel('h1n');
 axis([0 100 -2 2]);

零点越靠近极点，单位脉冲响应的变化越缓慢，零点对极点有抵消作用。第4种有两个靠近polar point的zero point，抵消作用更明显

可以把全部图像画在一起观察，更直观

 clc;
 clear all;
 close all;
 A=[1,-1.6,0.9425];
 B1=[1,0,0];
 B2=[1,-0.3,0];
 B3=[1,-0.8,0];
 B4=[1,-1.6,0.8];
 z1=roots(B1) %zero-point
 z2=roots(B2) %zero-point
 z3=roots(B3) %zero-point
 z4=roots(B4) %zero-point
 p=roots(A) %polar-point
 pm=abs(p);
 if max(pm)<1
     disp('system is stable and causal'),
 else
     disp('system is not stable and causal'),
 end
 [h1n,n]=impz(B1,A,100); 
 [h2n,n]=impz(B2,A,100); 
 [h3n,n]=impz(B3,A,100); 
 [h4n,n]=impz(B4,A,100); 
 figure
 stem(n,h1n,'.','r');
 xlabel('n');
 ylabel('h1n');
 axis([0 100 -2 2]);
 hold on
 stem(n,h2n,'.','b');
 xlabel('n');
 ylabel('h2n');
 axis([0 100 -2 2]);
 hold on
 stem(n,h3n,'.','k');
 xlabel('n');
 ylabel('h3n');
 axis([0 100 -2 2]);
 hold on
 stem(n,h4n,'.','g');
 xlabel('n');
 ylabel('h4n');
 axis([0 100 -2 2]);
 hold off