2. (a) For each sample of a discrete time signal x[n] as input, a system S…

2. (a) For each sample of a discrete time signal x[n] as input, a system S outputs the value y[n- . Determine whether the system S is i. linear ii. time-invariant 1ll. causal iv. stable Each of your answers should be supported by justification. In other words, show your reasoning (b) Consider a stable linear time-invariant (LTI) system with transfer function H(z). It is required to design a LTI compensator system G(z) that is in cascade with H(z) such that the overall system transfer function is given by Az-k,le, the overall system represents a constant gain with a pure delay of k 2 0 samples. Under what conditions is G(z) a stable filter? If G(z) not stable under any circumstances, explain why not.