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

For a periodic signal v(t) = 30 sin 100t + 10cos 300t + 6sin $${\rm{(500t + }}\,\pi /4)$$, the fundamental frequency in rad/s 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