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Two discrete time systems with impulse responses h1[n] = δ[n − 1] and h2[n] = δ[n − 2] are connected in cascade. The overall impulse response of the cascaded system is

1. δ[n − 1] + δ[n − 2]
2. δ[n − 4]
3. δ[n − 3]
4. δ[n − 1] δ[n − 2]

Correct answer: δ[n − 3]

Solution

The overall impulse response of two systems in cascade is found by convolving their individual impulse responses. Convolving h1[n] = δ[n − 1] with h2[n] = δ[n − 2] results in δ[n − 3], which represents the combined effect of the two systems.

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