Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is

A system with the transfer function $${{Y(s)} \over {X(s)}} = {s \over {s + p}}\,\,$$ has an output
$$y(t) = \cos \left( {2t - {\pi \over 3}} \right)\,$$ for the input signal
$$x(t) = p\cos \left( {2t - {\pi \over 2}} \right)$$. Then, the system parameter 'p' is

The Nyquist sampling rate for the signal $$s(t) = {{\sin \,(500\pi t)} \over {\pi \,t}} \times {{\sin \,(700\pi t)} \over {\pi \,t}}$$ is given by

Consider an angle modutated signal $$x(t) = 6\,\,\cos \,[2\,\pi \, \times {10^6}t + 2\sin (8000\pi t)\,4\cos (8000\pi t)]$$ V.

The average power of x(t) is