Let x(t) = sin 2 (2t), a periodic signal of fundamental period T 0 = 0.5, and

Let x(t) = sin²(2πt), a periodic signal of fundamental period T₀ = 0.5, and y(t) = |sin(2π t)|also periodic of the same fundamental period.

(a) A trigonometric identity gives that x(t) = 0.5[1 − cos(4π t)]. Use this result to find its complex exponential Fourier series.

(b) Use the Laplace transform to find the Fourier series of y(t).

(c) Are x(t) and y(t) identical? Explain.

(d) Indicate how you would use an ideal low-pass filter to get a dc source from x(t) and y(t). Indicate the bandwidth and the magnitude of the filters. Which of these two signals is used for generating full-waved rectified dc source?