Consider the discrete-time system F = L + N where L{.} is a linear time-invariant discrete-time system (x-1, x0, x1, · · ) and y = (·, Y-1, yo, y₁, ) = and N{} is given by the rule: if y = N{x} where x then, for all k, Yk = if |xk| ≤ 1, otherwise. | x² – - Xk, (a) (5 points) Prove that F is not linear. Also explain intuitively why F is not linear. (b) (5 points) Is F time invariant? You need not prove your answer mathematically, but you must give a rigorous justification to be awarded marks. (c) (5 points) Because F is not linear, generally speaking we cannot give meaning to a frequency response for F. However, for a certain class of input signals, it is meaningful to give F a frequency response. For what class of input signals would this be, and how would we define the frequency response? Justify your answer; no marks without valid justification.