Two discrete-time linear time-invariant systems with impulse responses
h1[n] = δ[n - 1] + δ[n + 1] and h2[n] = δ[n] + δ[n - 1] are connected in cascade, where δ[n] is the Kronecker delta. The impulse response of the cascaded system is
1
δ[n - 1] δ[n] + δ[n + 1] δ[n - 1]
2
δ[n - 2] + δ[n + 1]
3
δ[n - 2] + δ[n - 1] + δ[n] + δ[n + 1]
4
δ[n] δ[n - 1] + δ[n - 2] δ[n + 1]