a. Compute the DTFT of the following signals, either directly or using its properties (below a is a fixed constant |a| < 1):

x_n = (1/a)ⁿu_-n

b. Consider the following pairs of signals x and y. For each pair determine if there is an LTI system for which y is the output when the corresponding x is the input. If such a system exists, determine the frequency response of an LTI system with the desired behaviour. If no such system exists, explain why.

x_n = (1/2)ⁿu_n , y_n = (1/4)ⁿu_n