Consider a discrete-time system whose input x[n] and output y[n] are related by...

Consider a discrete-time system whose input x[n] and output y[n] are related by

(a) Show that if this system satisfies the condition of initial rest (i.e., if x[n] = 0 for n < n₀, then y[n] = 0 for n < n₀), then it is linear and time invariant.

(b) Show that if this system does not satisfy the condition of initial rest, but instead uses the auxiliary condition y[0] = 0, it is not causal. [Hint: Use an approach similar to that used in Problem 2.35.]