Exercise 2. CONTINUOUS-TIME SIGNAL RECOVERED FROM FOURIER COEFFICIENTS

Consider two periodic signals, 7₁ (t) and 1₂(t). ₁ (t) has period 2 and its Fourier series coefficients are

al = a₁ = 2 and a = 0 for all k +1. 1₂(t) has period 3 and its Fourier series coefficients are

a₁ =j,a-1-j and ax = 0 for all k + +1.

(i) Plot x1(t) and x₂(t).

(ii) Consider a new signal y(t) = £₁(t) +12(t). Find the Fourier series representation of the signal y(t).