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Split a system to 2 second-order section: weird phase result.

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Tsung-Ju Yang
Tsung-Ju Yang 2017 年 6 月 20 日
編集済み: Tsung-Ju Yang 2017 年 6 月 20 日
I am trying to split a system with transfer function H(z)=0.0976(z-1)^2*(z+1)^2/((z-0.3575-0.5889i)*(z-0.3575+0.5889i)*(z-0.7686-0.3338i)(z-0.7686+0.3338i)) to 2 second order section. My codes are as below:
clearvars;
b0=0.0976;
b1=[1 -1];
b2=[1 1];
a1=[1 -0.3575-0.5889i];
a2=conj(a1);
a3=[1 -0.7686-0.3338i];
a4=conj(a3);
b=b0.*conv(conv(b1,b1),conv(b2,b2));
a=conv(conv(a1,a2),conv(a3,a4));
[r,p,k]=residuez(b,a)
zplane(b,a)
freqz(b,a)
sos=zp2sos(r,p,k);
freqz(sos(1,1:3),sos(1,4:6))
freqz(sos(2,1:3),sos(2,4:6))
My question is about the graphic of frequency response. The phase of 2 subsystems do not add up to the original system. For example, when frequency is near 1 (angular frequency pi), the the phase of two sub-systems both go to zero but the original system go to about -180 degree (-pi.) Do sum of the phase response of the sub-systems should be the same as the pashe response of original system? May you so kind to help he with this puzzle?
The frequency response of original system
The frequency response of subsystem 1:
The frequency response of subsystem 2:

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