The Z-transform of δ[n] is 1, now the Z-transform of δ[n + 5] will be Z⁵ , by the property that if Z-transform of x[n] is X(Z) then the Z-transform of x[n-m] will be . . The region of convergence in this case is the entire z plane except    

(b) δ[n - 5] 

The Z-transform of δ[n] is 1, now the Z-transform of δ[n - 5] will be Z^-5 , by the property that if Z-transform of x[n] is X(Z) then the Z-transform of x[n-m] will be  . The region of convergence in this case is the entire z plane except

(c) (-1)ⁿu[n]

    has the Z-transform  hence the sequence (-1)ⁿu[n] will have the Z-transform  with the region of convergence

(d)          

 hence from combining the shifting property and the above used

property we can get the Z-transform to be as follows . The region of convergence will be    note that infinity is not in the ROC

(e)

If the X(Z) is the Z-transform of x[n] then we shall use the following properties to solve the above problem.

1. Z-transform of x[n-m] will be  .  The ROC  is all Z except 0( if m > 0) or infinity(if m < 0 )    

2. has the Z-transform   The ROC is

Hence the Z-Transform will be,  (in k, we now shift it by m = -1)

Hence the final transform will be  with region of convergence .

(f)

, hence now the

Z-transform using a procedure similar to the one above will be

    

 

By the shifting property and the property   has the Z-transform ,

we get the Z-transform to be   with the region of convergence