$5)$ Consider a LTI and continuous time system whose impulse response is given as:

$\backslash [$

h$($t$)$

$\backslash ]$

a$)(15$ Pts$.)$ Determine the output of this system when the input is an impulse train starting at $\backslash (\backslash$mathrm$\{$t$\}=2\backslash )$ with separations $\backslash (\backslash$mathrm$\{$T$\}=1\backslash )$ :

b$)(15$ Pts$.)$ Suppose that $"$an unknown" input $\backslash (\backslash$mathrm$\{$x$\}(\backslash$mathrm$\{$t$\})\backslash )$ is applied to the above system $\backslash (\backslash$mathrm$\{$h$\}(\backslash$mathrm$\{$t$\})\backslash ),$ and the following periodical output is observed:

By inspection $($guess$),$ determine what the input $\backslash ($ x$($t$)\backslash )$ would be to produce this $\backslash ($ y$($t$)\backslash )$ with the given $\backslash ($ h$($t$)\backslash ).$

Hint: The since the output is periodic, the input must also be a periodic signal.