Determine the Fourier series coefficients of the following periodic discrete-time signals

(a) x₁ [n] = 1 − cos(2πn/3), x₂[n] = 2 + cos(8πn/3), x₃[n] = 3 − cos(2πn/3) + cos(8πn/3), x₄ [n] = 2 + cos(8πn/3) + cos(2πn/3), x₅ [n] = cos(πn/3) + ( − 1)ⁿ.

(b)

(i) y[n] has a fundamental period N = 3 and a period  y₁[n] = (0.5)ⁿ for n = 0, 1, 2

(ii) v[n] has a fundamental period N = 5 and a period  v₁[n] = (0.5)^|n| for – 2 ≤ n ≤ 2

(iii) w[n] has a fundamental period N = 4 and a period  w₁[n] = 1 + (0.5)ⁿ for 0 ≤ n ≤ 3.

Indicate for each its fundamental frequency.