To sketch the magnitude of the filter, we find h(n) using iteration method.

h(0) = 2 δ(0) + 3 δ(-1) + 4 δ(-3) + δ(-4) = 2

h(1) = 2 δ(1) + 3 δ(0) + 4 δ(-2) + δ(-3) = 3

h(2) = 2 δ(2) + 3 δ(1) + 4 δ(-1) + δ(-2) = 0

h(3) = 2 δ(3) + 3 δ(2) + 4 δ(0) + δ(-1) = 4

h(4) = 2 δ(4) + 3 δ(3) + 4 δ(1) + δ(0) = 1

h(5) = 2 δ(5) + 3 δ(4) + 4 δ(2) + δ(1) = 0

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h(n) = {2, 3, 0, 4, 1, 0, 0, 0, . . . . }

The impulse response exists only for finite values of n.

Hence the name finite impulse response system(FIR).

This is a system without feedback