Let x(t) be a continuous-time signal, and let Yl (t) = x(2t) and Y2(t) = x(t/2). The signal y 1 (t).

Let x(t) be a continuous-time signal, and let Yl (t) = x(2t) and Y2(t) = x(t/2). The signal y1 (t) represents a speeded up version of x(t) in the sense that the duration of the signal is cut in half. Similarly, y2(t) represents a slowed down version of x(t) in the sense that the duration of the signal is doubled. Consider .the following statements: (1) If x(t) is periodic, then y1(t) is periodic. (2) If Yl (t) is periodic, then x(t) is periodic. (3) If x(t) is periodic, then y2(t) is periodic. (4) If y2(t) is periodic, then x(t) is periodic. For each of these statements,
Let x(t) be a continuous-time signal, and let Yl (t) = x(2t) and Y2(t) = x(t/2). The signal y1 (t) represents a speeded up version of x(t) in the sense that the duration of the signal is cut in half. Similarly, y2(t) represents a slowed down version of x(t) in the sense that the duration of the signal is doubled. Consider .the following statements: (1) If x(t) is periodic, then y1(t) is periodic. (2) If Yl (t) is periodic, then x(t) is periodic. (3) If x(t) is periodic, then y2(t) is periodic. (4) If y2(t) is periodic, then x(t) 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, produc~ a counterexample to it.

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