Digital Signal Processing Reference
In-Depth Information
3.2.7
Filter Length after Quantization
In the process of quantizing the filter, several coefficients may be rounded to zero
at the starting or ending of the filter; these must be discarded. The effective filter
length
L
q
is the minimum number of consecutive nonzero coefficients after
quantization. In this case, however, the lower bound
L
q
has been determined to be
2
L
q
≥
pB
+
qB
+
r
(3.11)
where
p
,
q
, and
r
are constants, and
B
is the bit size. Again,
L
q
is somewhat
sensitive to frequency, as above and we have used only those observations which
would give the smallest number of nonzero coefficients after quantization. Figure
3.9(a) shows a typical response between effective filter length and bit size. Table
3.4 gives the values for a range of filter starting lengths.
Table 3.4
Coefficients for Effective Filter Length versus Bit Size
for Various Filter Starting Lengths
Starting filter
length,
L
+1
p
(bit
-2
)
q
(bit
-1
)
r
99
-0.51
19.9
-93.9
155
-0.4
19.2
-69.5
255
-0.49
27.9
-105.7
3.3 ASPECTS OF FILTER COEFFICIENT FORMAT AND LAYOUT
Some aspects pertaining to the layout of the filter in the following pages are given
in this section. A description of the identifier, step response, and impulse response
function is noted.
3.3.1
Identifier
The identifier is the name given to the filter. The filter identifier is found at the top
of the page and follows the format:
LPF
nnn
F
m.m
LPF
Low-pass filter
nnn
Number of filter coefficients (i.e., its filter length)
F
Normalized frequency
Cut-off frequency value
m.m
