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

The transfer function of a discrete time LTI system is given by
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$

Consider the following statements:
S1: The system is stable and causal for $$ROC:\,\,\,\left| z \right| > \,1/2$$
S2: The system is stable but not causal for $$ROC:\,\,\,\left| z \right| < \,1/4$$
S3: The system is neither stable nor causal for $$ROC:\,\,1/4\, < \,\left| z \right| < \,{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$

Which one of the following statements is valid?

Two discrete time systems with impulse responses $${h_1}\left[ n \right]\, = \delta \left[ {n - 1} \right]$$ and $${h_2}\left[ n \right]\, = \delta \left[ {n - 2} \right]$$ are connected in cascade. The overall impulse response of the cascaded system is

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