Let x(t) be a continuous-time signal, and let The signal y1 (t) represents a sp...

Let x(t) be a continuous-time signal, and let

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 represents a slowed down version of x(t) in the sense that the duration of the signal is doubled. Consider the following statements:

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.