Digital Signal Processing Reference
In-Depth Information
120
(
a
)
(
b
)
L+1 = 255
99
1
100
55
80
0.75
F
-3dB
60
W
0.5
40
0.25
20
C
0
0
0
0.2
0.4
0.6
0
100
200
300
Normalised Frequency,
F
Length,
L
+1
Normalized Frequency,
F
Figure 5.1.
(a)
Parameter description and (b) a characteristic of band-pass filters.
B
1
h
(
2
1
(5.1)
h
=
ROUND
k
k
,
B
512
W
Here
h
,
is the new
B
-bit representation of the filter coefficients
h
k
,
W
is the
-6 dB bandwidth of the filter, and
ROUND
(
x
) is the nearest integer to
x
.
B
5.1.3
Band-Pass Filter Gain
G
The filter gain
G
of
h
,
in (5.1) is
B
B
1
(
2
1
(5.2)
G
=
512
W
and is the amount by which the input signal will be amplified on the filter output.
5.1.4
General Characteristics
Some of the general filter characteristics have been alluded to in our discussion on
low-pass filters. Like low-pass and high-pass filters, the bandwidth
W
for band-
pass filters is well defined as the normalized width at 0.5 (i.e. the -6 dB level). As
Figure 5.1(a) shows for a given width
W
, the edge transitions of all band-pass
filters cross at the -6 dB level, thereby guaranteeing this parameter.
