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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 />

The frequency response is given by<br />

exp( j2W)<br />

− 2r1<br />

cosq1<br />

exp( jW)<br />

+ r<br />

H ( W)<br />

=<br />

exp( j2W)<br />

− 2r<br />

cosq<br />

exp( jW)<br />

+ r<br />

2<br />

2<br />

2<br />

1<br />

2<br />

2<br />

where if r = 1<br />

1 there will be a frequency rejection at W = q1<br />

.<br />

The gain is<br />

H ( W)<br />

=<br />

2<br />

2<br />

2<br />

{( 1−<br />

2r1<br />

cosq1<br />

cosW + r1<br />

cos 2W) + ( 2r1<br />

cosq1<br />

sin W − r1<br />

sin 2W)<br />

}<br />

2<br />

2<br />

2<br />

2<br />

( 1−<br />

2r<br />

cosq<br />

cosW + r cos 2W) + ( 2r<br />

cosq<br />

sin W − r sin 2W)<br />

2 1/ 2<br />

{ } 1/ 2<br />

2 2<br />

2<br />

2 2<br />

2<br />

A summary if its frequency properties in relation <strong>to</strong> the zeros <strong>and</strong> poles is listed in Table 5.3.<br />

<br />

<br />

<br />

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