Introduction to Digital Signal and System Analysis - Tutorsindia

Introduction to Digital Signal and System Analysis
Frequency Domain Analysis
The frequency response is:
1−
exp( − jΩ)
H ( Ω)
=
1+
0.8exp( − jΩ)
or
1−
cosΩ + j sin Ω
H ( Ω)
=
1+
0.8cos Ω − 0.8 j sin Ω
Its magnitude is
H ( Ω)
=
1−
exp( − jΩ)
1+
0.8exp( − jΩ)
=
2
2
{( 1−
cos Ω) + ( sin Ω)
}
2
( 1+
0.8cos Ω) + ( 0.8sin Ω)
1/ 2
2
{ }
1/ 2
2 − 2cos Ω
=
1.64
+ 1.6cosΩ
1/ 2
And the phase
Φ
H
⎛ sin W ⎞
( W)
= arc tan⎜
⎟ − arc
⎝1
− cos W ⎠
⎛ − 0.8sin W ⎞
tan⎜
⎟
⎝1
+ 0.8cos W ⎠ . See Figure 4.7.
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