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Signals and Systems by Smarajit Ghosh

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ADDITIONAL SOLVED EXAMPLES

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

 

image

Solution

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

 

image

 

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) = n − 1u(n)
  2. x(n) = u(n) − u(n − 4)
  3. x(n) = n[u(n) − u(n − 4)]

Solution

  1. We know that

     

    image

     

    Differentiating both sides ...

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