Introduction to Digital Signal and System Analysis - Tutorsindia
Introduction to Digital Signal and System Analysis - Tutorsindia
Introduction to Digital Signal and System Analysis - Tutorsindia
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<strong>Introduction</strong> <strong>to</strong> <strong>Digital</strong> <strong>Signal</strong> <strong>and</strong> <strong>System</strong> <strong>Analysis</strong><br />
Z Domain <strong>Analysis</strong><br />
5 2<br />
Example 5.5. Find the zeros <strong>and</strong> poles for a z-transform X ( z)<br />
= ( z −1)(<br />
z + 1)<br />
Note<br />
5<br />
z − 1 = 0 has 5 complex roots.<br />
Since the rule for calculating roots for complex numbers is<br />
q + 2kp<br />
n<br />
1/ n<br />
( exp( jq<br />
)) = exp( j ) k = 0,1,..., n − 1<br />
Therefore, the 5 roots are<br />
(1)<br />
1/5<br />
2kp<br />
= k<br />
5<br />
1/5<br />
( exp( j0)<br />
) = exp( j ) = 0,1,..., 4<br />
2p<br />
4p<br />
6p<br />
8p<br />
In the z-transform, there are 7 zeros: 1,exp( j ), exp( j ), exp( j ), exp( j ) , j,-j<br />
5 5 5 5<br />
There is no pole in this case as denomina<strong>to</strong>r is 1. See Figure 5.5.<br />
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