A random process is defined as Y(t) = X (t) + X(t - T), where X (t) is a wide-sense stationary random process with auto correlation function R_X(T) and power spectral density S_x (f).

(a) Show that R_Y(τ) = 2R_X(τ) + R_X(τ + T) + R_X(τ - T).

(b) Show that S_Y(f) = 4S_X (f) cos²(πfT).

(c) If X (t) has auto correlation function R_X(τ) = 5Λ(τ) where Λ(τ) is the unit-area triangular function, and T = 0.5, find and sketch the power spectral density of Y(t) as defined in the problem statement.