Let x (n) be a discrete-time signal, and let The signal y1 [n] and y2 [n] respe...

Let x (n) be a discrete-time signal, and let

The signal y₁ [n] and y₂ [n] respectively represent in some sense the speeded up and slowed down versions of x[n]. However, it should be noted that the discrete-time notions of speeded up and slowed down have subtle differences with respect to their continuous-time counterparts. 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.