Through the system, the following transformations are made:
$ e^{2jt} \to t e^{-2jt} $
$ e^{2jt} \to t e^{-2jt} $
By observation, we know the system multiplies by t and is time reversing.
Given that:
$ \cos{t} = \frac{\exp^{jt} + \exp{-jt}}{2} $
Then
\cos{2t} \to t \frac{\exp^{-2jt} + \exp{2jt}}{2} = t \cos{t} </math>
