We are interested in designing a dc voltage source. To do so, we full-wave rectify an AC voltage to obtain the signal x(t) =|cos(πt)|,−∞

(a) Specify the magnitude response |H(jΩ)|of the ideal low-pass filter so that only the dc component of x(t)is passed through. Let the phase response be ∠H(jΩ) = 0. Find the dc value of the full-wave rectified signal x(t), and determine the dc gain of the filter so that the output y(t) = 1.

(b) If the input to the ideal filter obtained above is a half-wave rectified signal, what would be the corresponding output y(t)?