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

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Tsung-Ju Yang 2017-6-20

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https://ww2.mathworks.cn/matlabcentral/answers/345554-split-a-system-to-2-second-order-section-weird-phase-result

编辑： Tsung-Ju Yang 2017-6-20

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