Question $5$:$(10$ marks$)$

For the circuit shown above:

$($a$)$ Determine the transfer function $\backslash (\backslash$mathrm$\{$H$\}(\backslash$mathrm$\{$s$\})\backslash )$ and the impulse response.

$($b$)$ Identify the type of filter and calculate the center frequency, the bandwidth and the quality factor.