Sketch the waveform (with properly marked axes) at the output of a matched filter matched for a signal s(t), of duration T, given by $$s(t) = \left\{ {\matrix{ {A\,\,\,\,for} & {0 \le t < {2 \over 3}T} \cr {0\,\,\,\,\,\,for} & {{2 \over 3}T \le t < T} \cr } } \right.$$

The pole-zero pattern of a certain filter is shown in the Fig. The filter must be of the following type.

The magnitude and phase transfer functions for a distortionless filter should respectively be:

Specify the filter type if its voltage transfer function H(s) is given by

H(s) = $${{K({s^2} + {\omega _0}^2)} \over {{s^2} + ({\omega _0}/Q)s + {\omega _0}^2}}$$