# Transfer Function

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1. A linear time-invariant discrete-time system is excited by the input x[n] = d[n] + 2u[n-1] (d represents δ(delta)). The resulting output response with zero initial conditions is y[n] = ((0.5)^n * u[n]). Determine the transfer function of the system.

2. 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] = (e^3n * x[n]).

3. Compute the z-Transform for the discrete-time signal x[n] = ((0.5)^n * n * u[n]).

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This posting contains the solution to the given problems. The expert examines z-transforms for discrete-time signals.

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1. A linear time-invariant discrete-time system is excited by the input x[n] = δ[n] + 2u[n-1]. The resulting ...

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