1
ECE 408
HOMEWORK #4 (CH. 13)
1.
The normalized analog pole locations of a filter is given by
S = -0.3689
S = -0.1845
±
j0.9231
There are three zeros at S =
∞
.
These poles and zeros are transformed to bandpass poles
and zeros.
(a) Find the frequency transformed bandpass poles and zeros when
ϖ
1
= 1.0691e+004
rad/s and
ϖ
2
= 1.6000e+004.
(b) Find the digital poles and zeros when the sampling rate is 8000 Hz.
2.
The normalized analog pole locations of a filter are given by
S = -0.6829,
S = -0.1484
±
j0.5532,
S = -0.4758
±
j0.4186
The locations for zeros are
S =
0
±
j1.0515,
S =
0
±
j1.7013,
S =
∞
These poles and zeros are transformed to bandstop poles and zeros.
(a) Find the frequency transformed bandstop poles and zeros when
ϖ
1
= 6.6274e+003
rad/s and
ϖ
2
= 2.3946e+004.
(b) Find the digital poles and zeros when the sampling rate is 8000 Hz.
(c) Find the constant term b
0
such that
1
1
=
=
z
)
z
(
H
3.
The normalized analog pole locations of a filter are given by

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