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Computing the Z-transform
1. For a discrete-time signal x[n] with the z-Transform X(z) = z/(8z^2-2z-1), find the z-Transform, V(z) for the signal v[n] = x[n] * x[n].
2. Compute the unit-pulse response h[n] for the discrete-time system y[n+2]2y[n+1]+y[n]=x[n] (for n = 0, 1, 2, 3).
3. Compute the z-transform of the discrete time signal defined by x[n] = δ[n] +5δ[n- 1].
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