Question

June 8, 2018 ECE 3222, Signal and Systems Extra Credit Problem 6. (20 Points) Let x(t) be a continuous-time signal, and let: ,)(21) and y(d) (/2) The signal yi() represents a speed up version of x() in the sense that duration of the signal is cut in half. Similarly, y2(t) represents a slowed down version of x(t) in the sense that duration of the signal is doubled. Consider the following statements: a) Ifx() is periodic, then yi) is periodic b) Ifyi(o) is periodic, then x() is periodic c) Ifx(o) is periodic, then y2(0) is periodic d) If y2(0)) is periodic, then x(o) is periodic For each of these statements, determine whether it is true, and if so, determine the relationship between the fundamental periods of the two signals considered in the statement. If the statement is not true, produce a counterexample to it.

Answer 1