Digital Signal Processing Reference
In-Depth Information
4.1.2
Filter Coefficient Quantization
The conversion formula from floating-point precision to
B
-bit word representation
is
B
1
h
(
2
1
(4.1)
h
=
k
ROUND
k
,
B
512
(
F
)
c
Here
k
,
ROUND
(
x
) is
the nearest integer to
x
, and
F
c
is the normalized cut-on frequency. Note that (4.1)
does not include the overshoot
Q
, since it plays no part in determining the extent
to which the filter output overshoots the maximum integer value 2
B-
1
when the
step input involves the said value.
h
is the new
B
-bit representation of the filter coefficient
h
k
,
B
4.1.3
Filter Gain
G
The filter gain
G
of
h
for the high-pass filters given on the following pages is
k
,
B
B
1
2
1
. (4.2)
G
=
512
(
F
)
c
This is the amount by which the input signal will be amplified on the filter output.
4.1.4
Choice of Cut-on Frequencies
F
c
The choice of cut-on frequencies
F
c
for the filters presented here was dictated by
the additional range of low-pass filters that it affords the user. All the filters
presented in this chapter can be converted to low-pass filters thereby extending the
range given in Chapter 3. The conversion formula from high-pass to low-pass is
L
h
k
+
1
HP
,
k
2
h
=
(4.3)
LP
,
k
L
h
512
k
=
+
1
L
HP
,
+
1
2
2
where
h
LP
and
h
HP
are the low-pass and high-pass filter coefficients, respectively.
4.2 LISTING OF HIGH-PASS FILTERS
Table 4.1 gives an overview of high-pass filters presented here. In general, the
characteristics exhibited by their low-pass counterparts, such as transition width
