Homework 3_ECE301Fall2008mboutin - A - B - C
We know that the system is linear, therefore, we can sum the inputs to equal the sum of outputs:
The input is
- $ x_{c}(t) = e^{2\times jt} + e^{-2\times jt} $
and the corresponding output is
- $ y_{c}(t) = t \times e^{-2jt} + t \times e^{2jt} $
We know by Euler's formula:
- $ \cos 2t = {e^{2jt} + e^{-2jt} \over 2} $
Finally, by the multiplication property of linear systems:
The input,
- $ {x_{c}(t) \over 2} = \cos 2t = {e^{2\times jt} + e^{-2\times jt} \over 2} $
will yield the output:
- $ {y_{c}(t) \over 2} = {t e^{-2jt} + t e^{2jt} \over 2} $
