Let a periodic signal x(t)with a fundamental frequency 0 = 2 have a period x 1

Let a periodic signal x(t)with a fundamental frequency Ω₀ = 2π have a period

x₁(t) = t[u (t) − u(t − 1)]

(a) Plot x(t), and indicate its fundamental period T₀.

(b) Compute the Fourier series coefficients of x(t)using their integral definition.

(c) Use the Laplace transform to compute the Fourier series coefficients X_k. Indicate how to compute the dc term.

(d) Suppose that y(t) = dx(t)/dt, find the Fourier transform of x(t) by means of the Fourier series coefficients Y_k of y(t). Explain.