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% exa060301.m    for example 6.3.1 and fig6.3.1 
% To explain how to design a Lagrang half-band filter; 
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clear; 
 
sum=4.5*4.5*3.5*3.5*2.5*2.5*1.5*1.5*0.5*0.5; 
d1=factorial(4)*factorial(5)*1; 
d2=factorial(3)*factorial(6)*3; 
d3=factorial(2)*factorial(7)*5; 
d4=factorial(1)*factorial(8)*7; 
d5=factorial(0)*factorial(9)*9; 
h(1)=sum/d1; 
h(3)=-sum/d2; 
h(5)=sum/d3; 
h(7)=-sum/d4; 
h(9)=sum/d5; 
p=[h(9),0,h(7),0,h(5),0,h(3),0,h(1),0.5,h(1),0,h(3),0,h(5),0,h(7),0,h(9)]; 
 
figure(1) 
subplot(221) 
zplane(p,1) 
 
[P0,w]= freqz(p,1,512,1); 
subplot(222) 
plot(w,abs(P0));grid; 
 
figure(2) 
stem(p);grid; 
 
save p.mat p;