The input to a channel is a band pass signal. It is obtained by linearly modulating a sinusoidal carrier with a signal- tone signal. The output of the channel due to this input is given by y(t) = (1/100) cos$$(100t - {10^{ - 6}})\,$$ cos$$({10^6}t - 1.56)$$. The group delay $$({t_g})$$ and the phase delay $$({t_p})$$, in seconds, of the channel are

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

The Nyquist sampling frequency (in Hz) of a signal given by $$16 \times {10^{4\,}}\,\sin {c^2}(400t)*{10^6}\,\sin {c^3}(100t)$$ is