The support of a period of a periodic signal relates inversely to the support of the line spectrum. Consider two periodic signals: x(t) of fundamental period T₀ = 2 and y(t) of fundamental period T₁ = 1, and with periods

x₁(t) = u(t) − u(t − 1) 0 ≤ t ≤ 2

y₁(t) = u(t) − u(t − 0.5) 0 ≤ t ≤ 1

(a) Find the Fourier series coefficients for x(t) and y(t).

(b) Use MATLAB to plot the magnitude line spectra of the two signals from 0 to 80π rad/sec. Plot them on the same figure so you can determine which has a broader support. Indicate which signal is smoother and explain how it relates to its line spectrum.