Let x a (t) = x b (t) = t 2 over (0 ≤ t ≤ 1). Notice, this statement does not require x a (t) = x b (t) for all t. (a) Define xa(t) as an even, periodic signal with period Ta = 2. Sketch xa(t) and...

(a) Define xa(t) as an even, periodic signal with period Ta = 2. Sketch xa(t) and determine its power.

(b) Design an odd, periodic signal x_b(t) with period T_b
= 3 and power equal to unity. Fully describe x_b(t) and sketch the signal over at least one full period. Hint: There are an infinite number of possible solutions to this problem – you only need to find one of them!

(c) Using your results from (a) and (b), create a complex-valued function x_c(t) = x_a(t) + jx_b(t). Determine whether or not this signal is periodic. If yes, determine the period T_c. If no, justify why the signal is not periodic. In either case, compute the power of x_c(t).