The waveform of a periodic signal x(t) is shown in the figure.

A signal g(t) is defined by $$g(t) = x\left( {{{t - 1} \over 2}} \right)$$.

The average power of g(t) is___________________________.

Consider the function $$g(t) = {e^{ - t}}\,\,\,\sin (2\pi t)\,u(t)$$ where u(t) is the unit step function. The area under g(t) is_______________.

The phase response of a passband waveform at receiver is given by $$\varphi \,(f) = - 2\,\pi \,\alpha \,(f - {f_c}) - \,2\pi \beta \,{f_c}$$

where $${f_c}$$ is the centre frequency, and $$\alpha $$ and $$\beta $$ are positive constants. The actual signal propagation delay from the trasmitter to receiver is

A discrete - time signal x[n] = $${\rm{sin(}}\,{\pi ^2}n)$$, n being an integer is