The Z-Transform

1. Compute the z-Transform for the discrete-time signal .

2. Compute the inverse z-Transform of the transform

3. A discrete-time system is give by the input/output difference equation y[n+2]-y[n+1]+y[n]=x[n+2]-x[n+1].  Is the system stable, marginally stable, or unstable?

4. Compute the pole for the transfer function

5. A system has the transfer function .

Is the system stable, marginally stable, or unstable?