Q1) Find the output $y(t)$ of an LTI system with impulse response $h(t)$ when driven by the input $x(t)$ in each of the following cases:
a) $h(t) = sinc(t)$ $x(t) = cos(2\pi f_0 t)$
b) $h(t) = sinc(t)$ $x(t) = sinc(t)$
c) $h(t) = \delta(t) + \delta'(t)$ $x(t) = e^{-\alpha |t|}, (\alpha > 0)$
d) $h(t) = e^{-\alpha t}u(t)$ $x(t) = e^{-\beta t}u(t) \quad (\alpha, \beta > 0)$
where $u(t)$ is the unit step function, $\delta'(t) = \frac{d\delta(t)}{dt}$, and $sinc(t) = \frac{sin(\pi t)}{\pi t}$.
