Examples of transform pairs

1. The sample impulse sequence
   

   

   (the only non-zero contribution to the sum comes from the term n=0 .)

2. The causal exponential
   

   

   where we use the infinite geometric sum formula :

   

   Thus the ROC is or |z|>|a| where a may be real or complex .

   

   To use the MATLAB Symbolic Math Toolbox to evalute this z-transform :
   

   x=('A*a^n')
   X=ztrans(x)

3. The anticausal exponential
   

   

   With a bit of fiddling using the geometric sum rule :

   

   (note the difference in ROC from 2. above. must converge for negative n so must converge for positive n so )