Let x(t) = 2 + 4 sin(3t) + 6 cos(8t + /3). This is a periodic signal. (a) Determine the average power Pav in x(t).

Let x(t) = 2 + 4 sin(3πt) + 6 cos(8πt + π/3). This is a periodic signal. 

(a) Determine the average power Pav in x(t). 

(b) Determine the fundamental frequency Ω0 of x(t). 

(c) Compute the CTFS coefficients ck and express them in the magnitude-phase format. Plot the magnitude, phase, and power spectra as a function of k Ω0. 

(d) Determine the average power of x(t) from the frequency domain and verify that it equals Pav in part (a) above.