The input to a matched filter is given by $$s(t) = \left\{ {\matrix{ {10\sin (2\pi \times {{10}^6}t),} & {0 < \left| t \right| < {{10}^{ - 4}}\sec } \cr 0 & {Otherwise} \cr } } \right.$$

The peak amplitude of the filter output is

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: