Z Transform

[Baidehi]

Can someone please help me out with this Z transform problem? I have just started with this chapter and got stuck here:
Find the Z transform of (n-1)u(n-1)

 

[jjx]

The key is to note that it contains a "time"-delayed shift. So if you first find the template

• x[ n ] = n*u[ n ]

from the table of transforms:

• Z{ x [ n ] } = X(z) = (z^-1) / ( 1 - z^-1)^2

A single time shift equals dividing by z thus

• Z{ x(n-1) } = X(z) / z

Then just fill in the template

• Z{x(n-1)} = (z^-2) / ( 1 - z^-1)^2 = 1 / ( z - 1 )^2