Digital Signal Processing Reference
In-Depth Information
1
1
(
a
)
(
b
)
F
c
= 0.9
0.9
0.9
L
+1 = 255
0.8
0.8
0.8
55
0.7
0.7
0.7
0.6
0.6
0.6
33
0.5
0.5
0.5
0.4
0.4
0.4
0.3
0.3
0.3
0.25
0.2
0.2
0.2
0.15
0.1
0.1
0.1
0
0
0
50
100
150
200
250
300
0
0.2
0.4
0.6
0.8
1
Filter Length,
L
+1
Cut-off Frequency,
F
c
Figure 3.1
(a)
Influence of filter length on the -3dB frequency. (b) Relationship between cut-off
frequency
F
c
and
F
-3dB
.
F
c
has been normalized with
f
N
.
3.1.2
Transition Width and Slope
The transition width of the low-pass filter is the frequency range over which the
response of the filter changes from 0 dB (linear scale value 1) to a chosen
attenuation level,
. Figure 3.2 shows the transition width. From a design point
of view such a definition is useful, but the transition width becomes slightly
dependent on the maximum attenuation in the rejection band. Another option,
±δ
1 +
δ
R
1
1
−
δ
90%
∆
F
Transition width
10%
+
δ
0
− δ
Normalised Frequency
Normalized Frequency,
F
Figure 3.2
Definition of transition width, ripple, and
∆
F
.
