Digital Signal Processing Reference
In-Depth Information
(a)
0.4
h
()
0.2
0
-0.2
-0.4
-0.6
0
5
10
15
20
n
(b)
(c)
1.2
H
()
1.2
H
()
ω
ω
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
200
400
600
800
1000
0
200
400
600
800
1000
ωπ
2
ωπ
2
(d)
(e)
1.2
1.2
H
()
ω
H
()
ω
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
200
400
600
800
1000
0
200
400
600
800
1000
ω2
ω2
Fig. 6.13 Impulse response (a) and filter frequency characteristics for: b N = 20, c as b, with
application of Hamming window, d N = 100, e as d, with application of Hamming window
;
H
ð
X
Þ¼
X
N
1
H
ð
k
Þ
sin N
2
pk
exp
j
N
1
2
X
2p
k
N
ð
6
:
51
Þ
N sin
X
2
p
N
k
¼
0
where X
¼
2p
f
S
.
It is seen that for fixed discrete frequency values (f
k
¼
kf
S
=
N) the assumed and
obtained values are the same. The spectra at other frequencies are given by (
6.51
).
If the differences between assumed continuous frequency and obtained one are
for any frequency too big, one can apply smoothing windows as described above.
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