Problem 4
A general deterministic system can be described by operator $ H $ that maps an input $ x(t) $ as a function of $ t $ to an output $ y(t) $.
Given two valid inputs
- $ x_1(t) \, $
- $ x_2(t) \, $
as well as their respective outputs
- $ y_1(t) = H \left \{ x_1(t) \right \} $
- $ y_2(t) = H \left \{ x_2(t) \right \} $
then a linear system must satisfy
- $ \alpha y_1(t) + \beta y_2(t) = H \left \{ \alpha x_1(t) + \beta x_2(t) \right \} $
for any scalar values $ \alpha \, $ and $ \beta \, $.
