For complex periodic signal:

$-\frac{8 T \left(2 T \omega \sin (2 t \omega )-e^{-\frac{t}{T}}+\cos (2 t \omega )\right)}{\alpha ^2 \left(4 T^2 \omega
 ^2+1\right)}$

where $T,\alpha,\omega$ - parameters, $t$ - time

*How to calculate the supremum in symbolic form?*

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This is what the `Limit` and `MaxLimit` commands show.

[![enter image description here](https://i.stack.imgur.com/Hxu95.png)](https://i.stack.imgur.com/Hxu95.png)

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And here is the expression for signal itself

```
s=-((8 T (-E^(-(t/T)) + Cos[2 t \[Omega]] + 
    2 T \[Omega] Sin[2 t \[Omega]]))/(\[Alpha]^2 (1 + 
    4 T^2 \[Omega]^2)))

```