Example 3.2.1: Finding the transfer function
Find the transfer function H(z) of the IIR system (Infinite Impulse Response) h(n) = ()n u(n)

Solution

We have h(n) = {1, 1/2, 1/4, ...}; the value at n = 0 marked bold, and

H(z) = h(n) z-n = ()n u(n) z-n

        = ()n z-n = ( z-1)n          sum of a Geometric series
      = 1 ,   | z-1 | < 1     <=> |z| >
1 - z-1
You can find this from Tables,too.


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