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enter image description here

  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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    $\begingroup$ You could use $y[k] = u[k]/U[k]$ where $U[k] = \max(U[k - 1], u[k])$. This will be wrong at the start but if that is acceptable it would be a simple solution that will be correct once the steady state value is reached for the first time. $\endgroup$
    – SampleTime
    Commented May 4, 2021 at 15:26
  • $\begingroup$ @SampleTime Good idea at first glance. Is there a continuous analogue of your proposal? $\endgroup$
    – dtn
    Commented May 4, 2021 at 15:28
  • $\begingroup$ I am not sure, maybe you can convert it to continuous time. But this is maybe difficult because it is a nonlinear equation. $\endgroup$
    – SampleTime
    Commented May 4, 2021 at 15:30
  • $\begingroup$ @SampleTime ibb.co/dK4cTPX Or maybe there is some trick that allows using the input signal and its sign to get at the output a signal of the same shape, but scaled? $+- 1/2$ is just my fantasy. :) $\endgroup$
    – dtn
    Commented May 4, 2021 at 15:35
  • $\begingroup$ I don't see how you would use the sign to identify the steady state value of $1/2$ in your image. The sign doesn't tell you anything new about the steady state value (except its sign of course). $\endgroup$
    – SampleTime
    Commented May 4, 2021 at 17:26

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