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I have the input and the output of a system and I want to determine the transfer function of it. I am using Ident Tool from Matlab. How is it more ok: to normalize the output and the input between 0 and 1 or to leave it as they are?

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    $\begingroup$ Why would you change the output at all for a given input? If you do before running the system ID functions, you'll get the wrong gain (at least). Selecting the right level of input is probably OK... but normalizing it to be between 0 and 1 is probably not the right thing to do either: you'll over-emphasize the DC component of the system to the system ID function. $\endgroup$ – Peter K. Apr 7 '16 at 11:26
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For what I know there is no reason to normalize data in general, if you use least squares like methods, all you need is that your input is persistently exciting, in the sense that the Hankel matrix $H$ of the observations must be such that $H^T H$ is nonsingular.

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If you system is linear, the linear property holds: multiplying the input by $\lambda$ should yield an output multiplied by $\lambda$. So you should not normalize I/Os independently, which happens when you normalize them between $0$ and $1$, since you will be using the $\min$ and $\max$ separately.

However, it is possible to normalize them to the same units, if for some reason, inputs are in mV and output in V, for instance.

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