X(z) = 1 – 3z– 1, Y (z) = 1 + 2z–2 are Z- transforms

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X(z) = 1 – 3z^{– 1}, Y (z) = 1 + 2z^–2 are Z- transforms of two signals x[n], y[n] respectively. A linear time invariant system has the impulse response h[n] defined by these two signals as h[n] = x[n– 1]*y[n] where * denotes discrete time convolution. Then the output of the system for the input δ [n – 1]

1. has Z – transform z^{– 1} X (z) Y(z)
2. equals δ[n - 2] – 3δ[n – 3] + 2δ[n – 4] – 6δ[n – 5]
3. has Z – transform 1 – 3z^{– 1} + 2z^–2 – 6z^–3
4. does not satisfy any of the above three.

Correct Option: B

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