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ECE 101  Linear Systems, Winter 2009
Lab # 5 Solutions
(send comments/questions to [email protected])
Problem 5.4(a), BDS
The transform
H
id
(
e
jω
)
is periodic with period 2
π
. Thus, since the desired
lowpass ﬁlter will satisfy
H
id
= 1 for

ω

< π/
2 over the range

π < ω < π
,
it follows that over the range 0
< ω <
2
π
, it will be nonzero for 0
< ω < π/
2
and 3
π/
2
< ω <
2
π
.
1
0
0
π
π
2
Η
(
)
e
ω
j
id
1
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View Full Document Problem 5.4(b), BDS
From the 9 samples taken at spacings of (2
/
9)
π
in frequency, an interpola
tion of
ﬂ
ﬂ
H
(
e
jω
)
ﬂ
ﬂ
can be constructed and plotted. As can be seen, it contains
the general features of the ideal ﬁlter.
0.5
1
1.5
2
0.2
0.4
0.6
0.8
1
1.2
1.4
Η(
)
e
ω
j
ω/π
2
Problem 5.4(c), BDS
We are constrained to design an FIR ﬁlter that is both causal and of ﬁnite
duration in
n
. In order to obtain a unique solution based on the samples
speciﬁed in part (
b
), we set the number of nonzero
n
values to
N
= 9 (i.e.,
set
N
to the number of frequency samples). It follows that
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This note was uploaded on 02/24/2010 for the course ECE ECE25 taught by Professor Bill lin during the Spring '09 term at UCSD.
 Spring '09
 bill lin

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