Consider a periodic signal x(t) = 0.5 + 4 cos(2 t) 8 cos(4 t)

Consider a periodic signal

x(t) = 0.5 + 4 cos(2π t) − 8 cos(4π t)           − ∞

(a) Determine the fundamental frequency Ω_­0 of x(t).

(b) Find the Fourier series coefficients {X_k} and carefully plot their magnitude, and phase spectra. According to the magnitude line spectrum at what frequency is the power of x(t) the largest?

(c) When x(t) is passed through a filter with transfer function H(s) the output of the filter is y(t) = 2−2 sin(2π t). Determine the values of H(jΩ) at Ω = 0, 2π, 4π rad/sec.