Signals and Systems

ADDITIONAL SOLVED EXAMPLES

Example 6.12 Find the z-transform and its ROC of the following sequence:

 

Solution

The z-transform X(z) of x(n) is given by

 

 

Therefore, X(z) will be finite if and only if z is not equal to 0 or ∞. Its ROC is given by 0 < |z| < ∞.

Example 6.13 Find the z-transform of the following sequences:

1. x(n) = nα^{n − 1}u(n)
2. x(n) = u(n) − u(n − 4)
3. x(n) = n[u(n) − u(n − 4)]

Solution

1. We know that

    

   

    

   Differentiating both sides ...