Introduction to Digital Signal and System Analysis - Tutorsindia

Introduction to Digital Signal and System Analysis
Z Domain Analysis
H
exp( j2W)
W)
=
exp( j2W)
− 2r
cosq
exp( jW)
+ r
1
=
1−
2r
cosq
exp( − jW)
+ r
2
(
2
2
exp( − j2W)
The gain is
H
2
( W)
=
1
2
2
2
2
{( 1−
2r
cosq
cos W + r cos 2W) + ( 2r
cosq
sin W − r sin 2W)
} 1 / 2
The peak gain occurs at
W = ± q :
G
max
=
H ( q )
2
=
1
2 2
2
2
2
{( 1 − 2r
cos q + r cos 2q
) + ( 2r
cosq
sinq
− r sin 2ϑ
) } 1/ 2
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