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When you see software packages that read in data from sensing equipment, does the software do something to inverse the transfer function?

Correct me if I'm wrong in my understanding, but this is how I see it:

The sensor takes in input signal $x(t)$ and the sensor has some frequency response governed by the Transfer function of the sensor which alters the signal $x(t)$ to some deformed signal $y(t)$. So if anybody wanted to know about the actual signal would they inverse the Transfer function? And is this on top of other calibration values? Gain etc..?

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  • $\begingroup$ you need to read the documentation provided with the software to know what it does. a commercial product will have applications and sales engineers to help with specific issues. Free software typically has web groups where users share their expertise. your question is too broad to meaningfully answer. $\endgroup$ – Stanley Pawlukiewicz Sep 10 at 16:43
  • $\begingroup$ Can you please tell me why I need to be more specific, are there conditions where you do/don't inverse the transfer function? Unfortunately there is no software for me to check the documentation, im trying to write my own, and the sensor is an accelerometer if this helps $\endgroup$ – Stephen Jackson Sep 10 at 17:35
  • $\begingroup$ what software packages are we supposed to have seen is one way to make your question more specific $\endgroup$ – Stanley Pawlukiewicz Sep 10 at 23:58
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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 applications you might not care about it that much and leave it in or only partially compensate it.

What's though true is that in general you cannot completely eliminate the effect of your sensing equipment. By the way it filters the "true" signal $x(t)$, some of its components might be filtered out and be lost completely. As a simple example: practically all real systems have some sort of low-pass characteristic so that very high frequency components will not do anything to it and thus never show up in $y(t)$. If you excite a 1 kHz low-pass system with a 1 GHz input signal, you cannot hope to get it back by inverting the low-pass characteristic, you'd have to divide by zero essentially.

There may be other reasons you would not want to compensate. Say your system does have a very small gain at some particular frequency. Then if you try to invert this behaviour, you'll need to amplify this particular frequency a lot. This would mean that any unwanted component, such as noise, would be strongly amplified at this particular spot. In applications like this you might want to do a partial calibration, where you do correct for the transfer function in a certain frequency region of interest only, and ignore the rest of it.

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