The computation of the Fourier series coefficients is helped by the relation between the formula for these coefficients and the Laplace transform of a period of the periodic signal.

(a) A periodic signal x(t) of period T₀ = 2 sec., has as a period the signal x₁(t) = u(t) − u(t − 1). Use the Laplace transform of x₁(t) to obtain the Fourier coefficients of x(t).

(b) Use MATLAB to approximate x(t) with 40 harmonics, plot the approximate signal x̂(t) and its magnitude line spectrum.