Consider a system for which the input x[n] and the output y[n] satisfy the following rel...

Consider a system for which the input x[n] and the output y[n] satisfy the following relation.

(a) For x[n] = δ[n], show that a particular sequence satisfying the difference equation is

(b) Determine the homogeneous solution(s) to the difference equation specified in Eq. (P2.25-1).

(c) Determine y[n] for −2 ≤ n ≤ 2 when x[n] is equal to δ[n] in Eq. (P2.25-1) and the initial rest condition is assumed in solving the difference equation. Note that the initial rest condition implies the system described by Eq. (P2.25-1) is causal.