Consider the following pairs of signals x[n] and y[n]. For each pair, determine whether...

Consider the following pairs of signals x[n] and y[n]. For each pair, determine whether there is a discrete-time LTI system for which y[n] is the output when the corresponding x[n] is the input. If such a system exists, determine whether the system is unique (i.e., whether there is more than one LTI system with the given input-output pair). Also, determine the frequency response of an LTI system with the desired behavior. If no such LTI system exists for a given x[n], y[n] pair, explain why.