%  ex_13_03_1.m :  習題 13.3

clear all;
close all;

rmd=0.9;
b=[1 -1/rmd];
a=[1.000 -rmd];
[h,w] = freqz(b,a,512,1); 
g = abs(h);
% 
aq = truncation(a,4);
bq=truncation(b,4);
[hq,w] = freqz(bq,aq,512,1); 
gq = abs(hq);
figure('color','w')
subplot(221)
plot(w,g,'b',w,gq,'r:');grid
%
m_ra4=roots(aq)
m_rb4=roots(bq)
 
aq = truncation(a,8);
bq = truncation(b,8);
[hq,w] = freqz(bq,aq,512,1);
gq = abs(hq);
subplot(223)
plot(w,g,'b',w,gq,'r:');grid

m_ra8=roots(aq)
m_rb8=roots(bq)
 
rmd=0.98;
b=[1 -1/rmd];
a=[1.000 -rmd];
[h,w] = freqz(b,a,512,1); 
g = abs(h);
% 
aq = truncation(a,4);
bq=truncation(b,4);
[hq,w] = freqz(bq,aq,512,1); 
gq = (hq);
subplot(222)
plot(w,g,'b',w,gq,'r:');grid

m_r2a4=roots(aq)
m_r2b4=roots(bq)
 
aq = truncation(a,8);
bq = truncation(b,8);
 
[hq,w] = freqz(bq,aq,512,1);
gq = abs(hq);
subplot(224)
plot(w,g,'b',w,gq,'r:');grid

m_r2a8=roots(aq)
m_r2b8=roots(bq)