Digital Signal Processing Reference
In-Depth Information
0
120
0.1
(
a
)
(
b
)
A
q
L
q
-20
100
0.01
-40
80
-60
60
0.001
-80
40
0.0001
-100
20
-120
0
0.00001
0
5 10 15 20 25
Filter coefficient word size,
B
(bits)
0
5
10
15
20
25
Coefficient Word size,
B
(bits)
Figure 3.9
Upper bounds of (a) attenuation and effective filter length, and (b) ripple for 99-point filters
as a function of coefficient bit size.
3.2.6
Pass-Band Ripple after Filter Quantization
The upper bounds for pass-band ripple after quantization
R
q
is given by
R
q
≤
B
+
(3.10)
α
β
where
B
is the bit size and
are constants. The pass band ripple
R
q
is
slightly sensitive to frequency, and like the attenuation
A
q
above, the worst-case
observations have been used to determine the upper bounds. As such, almost all
filters will show a lower peak-to-peak ripple for a given word size than the linear
relationship suggested by (3.10). Figure 3.9 (b) shows a typical plot of the upper
bound peak-to-peak ripple against bit size. Table 3.3 gives the parameters
α
and
β
α
and
β
for various filter starting lengths.
Table 3.3
Coefficients for Ripple versus Bit Size
for Various Filter Starting Lengths*
Starting filter length,
L
+1
(dB)
99 -5.85 18.25
155 -5.9 22.0
255 -5.56 18.6
*See Section 3.1.4 for definition of pass-band ripple
R
.
α
(dB/bit)
β
