The bode plot of the cascaded connection of two discrete time systems is given an unexpected result. I'm using MATLAB 2017b. The unexpected Bode Plot obtained with MATLAB and the expected Bode Plot obtained with Wolfram Mathematica for the casacade system is illustrated below. What is the reason for the unexpected Bode Plot obtained with MATLAB? How can I get the same Bode Plot obtained with Wolfram Mathematica?
1-Considering the discrete time systems G1 and G2 whose bode plots are shown below:
2-The unexpected bode plot of the system G1*G2, which is the cascade connection of G1 and G2 is shown below:
3-The expected bode plot obtained with the software Wolfram Mathematica is shown below:
4-the script used in MATLAB is shown below:
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Ts = 1/39960;
num1 = 1.0e+02.*[0.031539179206086,-0.218479792518950,0.648677356726311,-1.070054451616472,1.059168924735488,-0.629079503155372,0.207587755626987,-0.029359469003776];
den1 = [1.0,-6.878539169404124,20.274720364621878,-33.195141325571285,32.604147581404845,-19.210710652654448,6.287177056909766,-0.881653855287863];
G1 = filt(num1, den1, Ts);
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num2 = [0,0,0.030214737804111,-0.106047418049407,0.152721406591927,-0.106047418049407,0.030214737804111]
den2 = [1.0,-4.192774816029949,7.580364905504299,-7.484428436489121,4.192774816029949,-1.256799136009598,0.160862666994420]
G2 = filt(num2, den2, Ts);
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G1G2 = series(G1,G2)
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figure
bode(G1,'b')
hold
bode(G2,'r')
h = gcr;
h.AxesGrid.Xunits = 'Hz';
grid on;
xlim([10,40000])
h2 = findobj(gcf,'type','line');
set(h2,'linewidth',1);
h2 = findobj(gcf,'type','text');
set(h2,'FontSize',12);
legend('G1','G2')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure
bode(G1G2,'m')
h = gcr;
h.AxesGrid.Xunits = 'Hz';
grid on;
xlim([10,40000])
h2 = findobj(gcf,'type','line');
set(h2,'linewidth',1);
h2 = findobj(gcf,'type','text');
set(h2,'FontSize',12);
legend('G1*G2')
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