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how "bode" calculate the phase of transfer function?

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saner chen
saner chen on 27 Mar 2019
There is a moving average filter:
in s and z domain:
their magnitude- w and phase -w characteristic are as follows:
(1)
it can be seen that if , then the second formula of (1) converges to the first one.
thus their phase-w curves should be the same.
however.
T = 5e-5;
N = 400;
Tw = N*T;
s = tf('s');
z = tf('z',T);
G = (1-exp(-Tw*s))/(Tw*s);
G2 = (1-z^(-N))/(1-z^(-1))/N;
bode(G,G2)
legend('continus','discrete')
untitled.png
the phase of G2 is much higher than G1.
So how "bode" calculate the phase? and is the figure is right if I didnt restrict the phase in[-180,180].
Is the phase pi/4 - 5*2*pi equal to pi/4 ?

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