# Matlab - Bode plot of discrete and continuous Function

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Martin Werner on 14 Oct 2019
Answered: Paul on 24 Feb 2023
I am rather new to Matlab and I just cant make sense of what I see in the bode plot of the continuous and discrete version of the same function. The bode plot of the continuous function looks as expected. However the bode plot of the discrete version has a phase offset of +90 degrees and the gain stays the same at lower frequencies. It's basically a lag compensator with an integrator. This is not the final result I am going for, but the easiest example I could think of to make the problem as clear as possible. Please note that I am using a rather high sampling rate of ~12 MHz, which is what I need in the final hardware design. The high sampling rate seems to be part of the problem. With lower sampling rates the frequency at which the bode plots differ gets shifted to the left.
Can anyone explain this behaviour and maybe how I can achieve a result that is closer to the continuous bode plot using the high sampling rate?
Code of the example:
FS = 48000*256;
T_sample = 1/FS;
accu = tf([0 1], [1 0]);
lag = tf([10 1], [100 1]);
lag_d = c2d(lag, T_sample, "zoh");
accu_d = c2d(accu, T_sample, "zoh");
bode(lag*accu, lag_d*accu_d);
##### 2 CommentsShow 1 older commentHide 1 older comment
Luca Ferro on 24 Feb 2023
it doesn't make any sense to bode plot a discrete transfer function.
Bode is defined in the Laplace domain (s) while discrete transfer functions are in the z domain.
It's like putting a cat in a pool and expecting it to behave like a fish.

Paul on 24 Feb 2023
One problem is that the discretization of the product is not the product of the discretization. But with T_sample so small, that's probably not the issue. It appears that bode is having a problem with numerical calculations in the tf form. Instead, use zpk. zpk is preferred over tf in most (all?) cases.
FS = 48000*256;
T_sample = 1/FS;
accu = tf([0 1], [1 0]);
lag = tf([10 1], [100 1]);
htf = lag*accu;
hzpk = zpk(lag)*zpk(accu);
hzpkd = c2d(hzpk,T_sample,'zoh');
%lag_d = c2d(lag, T_sample, "zoh");
%accu_d = c2d(accu, T_sample, "zoh");
bode(htf, hzpk, hzpkd);

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