For the signal x(t) = 4cos(800p t +p / 4) + 8cos(1200p t -p / 3) - 4cos(1600p t) :
(a) Sketch the double--sided spectrum of the signal, indicating the magnitude and phase of each component.
(b) What is the period of x(t)?
(c) If we define a new signal y(t) = x(t) + 5cos(1000p t +p / 2) , is the "system" y(t)=F(x(t)) linear or nonlinear? Why?
(d) Plot the spectrum of y(t). What is the period of y(t)?