Problem consider the signal xt 15cos015pit 14 3

Question

Problem: Consider the signal x(t) = 1.5cos(0.15π(t + 1.4)) + 3 cos(0.25π(t - 3)).

(a) Sketch the two-sided spectrum for x(t).

(b) Find the fundamental frequency f₀ (in Hz)

(c) Find the fundamental period T₀ (in seconds).

(d) Give two examples of a value for ω₀ such that the sum x(t) + cos (ω₀t) is not periodic.

(e) Solve the following equation for the delay t:

x(t) + x(t - t) = 0

if the answer is not unique, specify all possible solutions.