Digital Signal Processing Reference
In-Depth Information
where
w
(
n
) is the window function. In the case of the rectangular window function,
C
n
=
C
n
. The transfer function in (4.59) can then be written as
N
-
1
Â
¢
()
=¢
=
Hz
hz
i
-
i
(4.69)
i
0
where
hC
¢=
¢
0
£ £
i
2
Q
(4.70)
i
Qi
-
13 dB from
the peak of its mainlobe, resulting in oscillations with an amplitude of considerable
size. On the other hand, it has the narrowest mainlobe that can provide high selec-
tivity. The following window functions are commonly used in the design of FIR
filters [12].
The rectangular window has its highest sidelobe level, down by only
-
4.6.1 Hamming Window
The Hamming window function [12,25] is
(
)
054
.
+
046
.
cos
nQ
p
for
otherwise
nQ
£
Ó
()
=
wn
(4.71)
H
0
which has the highest or first sidelobe level at approximately
-
43 dB from the peak
of the main lobe.
4.6.2 Hanning Window
The Hanning or raised cosine window function is
(
)
05
.
+
05
.
cos
nQ
p
for
otherwise
nQ
£
Ó
()
=
wn
(4.72)
HA
0
which has the highest or first sidelobe level at approximately
-
31 dB from the peak
of the mainlobe.
4.6.3 Blackman Window
The Blackman window function is
(
)
+
(
)
0 42
.
+
0 5
.
cos
nQ
p
0 08
.
cos
2
nQ
p
nQ
£
Ó
()
=
wn
(4.73)
B
0
otherwise
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