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I think your question has nothing to do with "software", so I'll ignore this part, and only discuss the calibration part of it. Then again, your question is very broad and cannot be answered with yes or no: It really depends. In some applications you might want to try to invert as much of the transfer function of your sensor as possible. In other ...


Q1: You should ask yourself if $$\frac{z}{3z^2 - 4z + 1}\stackrel{?}{=}\frac{\frac 3 2}{z-1} - \frac{\frac 1 2 }{z-\frac 1 3}$$ really holds. You'll find out that you forgot to scale correctly. Q2: There is no reason to consider $X(z)/z$ instead of $X(z)$ in this case. And concerning your question about the anti-causal sequence, a multiplication by $z^{-...


Your two transfer functions are in parallel, i.e they simply add up. So your feedback transfer function is simply $G(z) = H_1(z)+H_2(z)$. You want to makes sure that the magnitude of $G(z)$ is smaller than one. and the overall closed loop transfer function is $$H(z) = \frac{Y(z)}{X(z)} = \frac{1}{1+H_1(z)+H_2(z)}$$


It does matter that $a=b=2$, because this gives a relatively nice looking solution. As mentioned in a comment, you should split up the given transfer function $H(s)$. But first, let's introduce a normalized variable $p$: $$p=\frac{s}{\omega_n}\tag{1}$$ Now we can write the given transfer function as $$\hat{H}(p)=\frac{2p^2+2p+1}{p^3+2p^2+2p+1}\tag{2}$$ ...

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