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  1. The input signal is limited and lies in range $[-U;+U]$. $U$ - unknown.
  2. The output signal must be rescaled to be in the range $[-1;+1]$, i.e. is $+1$ if the input is at steady-state $+U$, and $-1$ if the input at steady-state $-U$.
  3. Between $-1$ and $+1$ the output signal must also occupy some rescaled value.

What can be used as a block $ ??? $ for such a conversion? Is there a linear / non-linear filter that does this, and such and which is described by the differential equation?

Remarks: Red line, just my fantasy about how the input signal changes

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – hazzey
    May 4 at 16:20
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  • Input signal: ±U V.
  • Scaled output signal: ±1 V.
  • Required gain: $ \frac 1 U $.

schematic

Figure 1. Possible solutions.

  • If U > 1 then a simple potential divider may suffice. $ V_{OUT} = \frac {R_2}{R_1+R_2} $. Bear in mind that whatever follows this circuit may load it somewhat so keep the parallel combination value of R1 || R2 < 10% of the value of the following stage.

  • If U < 1 then a non-inverting amplifier is required. Gain is given by $ A = 1 + \frac {R_4}{R_3 + R_4} $.

Question Response
Is there a linear / non-linear filter that does this, ... A filter is for modifying a signal's frequency content. This is not what you are trying to do so a filter is not an appropriate solution.
... and such and which is described by the differential equation? You are looking for a simple attenuation or amplification function. There is no need for differential equations.
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  • $\begingroup$ Thank you for your answer. For some reason, it seemed to me that in your answer there is no important detail that I reflected in the question. $U$ - unknown. $\endgroup$
    – dtn
    May 4 at 14:31
  • $\begingroup$ For this reason, I am looking at more sophisticated devices and mathematical tricks. $\endgroup$
    – dtn
    May 4 at 14:33
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    $\begingroup$ It sounds like you want the equivalent of audio AGC (automatic gain control) but even there you still have to specify minimum and maximum signals and the AGC response time. i.e., You can get it to attenuate quickly so that the output doesn't overdrive but then you need to specify a recovery time when the input goes low. The problem is that the scale keeps changing so the output doesn't relate linearly to the input. $\endgroup$
    – Transistor
    May 4 at 14:51
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    $\begingroup$ @dtn, by the way, for AGC, the signal has to hit the min/max regularly enough for it to work. As far as analog signals go, it is best suited for something like a carrier signal that is modulated in some way. Compression in audio is another example. It would be inappropriate for something like a temperature measurement that is converted to a DC voltage. $\endgroup$
    – Pete W
    May 4 at 22:21
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    $\begingroup$ in my opinion, you should back up, zoom all the way out, and describe what you're really trying to do. Also it's better to ask this question at https://electronics.stackexchange.com/ $\endgroup$
    – Pete W
    May 5 at 11:59

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