Mathematical Introduction To Control Theory
By Shlomo Engelberg

10.3: Some Examples

10.3 Some Examples

In calculating z-transforms, it is often necessary to sum a geometric series. Recall that the geometric series is the sum:


and its sum is:


Let us consider the z-transform of several sequences.

  1. Let


    We find that:


  2. Let e(k) = a k. Then we find that:


  3. Similarly, if we let e( k) = e -ak, then we find that:


  4. Let e( k) = sin( ? k). Rewriting sin( ? k) as:


    we find that:


Copyright Imperial College Press 2005 under license agreement with Books24x7
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