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# Z-Transforms for Discrete-Time Signals

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1. Compute the s-Transform for the discrete-time signal x[n] = (0.5)(^n)nu[n].

2. Compute the z-Transform for the discrete-time signal x[n] = (0.25)(^-n)u[n-2].

3. For the discrete-time signal x[n] with the z-Transform X(z) = z/(8z^2 - 2z - 1) find the z-Transofmr, V(z) for the signal v[n] = e^(3n)x[n].

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#### Solution Preview

1. (a^n)nu(n) -> (az)/(z-a)^2
For this problem, a = 0.5.
Answer is b: (2z)/(2z-1)^2

2. x[n] = 16*(4^(n-2))u[n-2]
(a^n)u(n) -> z/(z-a) & ...

#### Solution Summary

Through step by step calculations, this solution calculates the transforms of the discrete-time signals.

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