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In-Depth Information
T A B L E 14 . 6
Coefficients for the four-tap
Daubechies low-pass filter.
h
0
0
.
4829629131445341
h
1
0
.
8365163037378079
h
2
0
.
2241438680420134
h
3
−
0
.
1294095225512604
3
2
1
0
0
0.5
1
1.5
2
2.5
3
Two-band
3
2
1
0
0
0.5
1
1.5
2
2.5
3
Four-band
3
2
1
0
0
0.5
1
1.5
2
2.5
3
Eight-band
F I GU R E 14 . 20
Spectral characteristics at points A, B, and C.
If
H
L
(
corresponds to a 22-tap filter! However, this
is a severely constrained filter because it was generated using only four coefficients. If we had
set out to design a 22-tap filter from scratch, we would have had significantly more freedom
in selecting the coefficients. This is a strong motivation for designing filters directly for the
M
-band case.
An
M
-band filter bank has two sets of filters that are arranged as shown in Figure
14.7
.
The input signal
x
z
)
corresponds to a 4-tap filter, then
A
(
z
)
(
n
)
is split into
M
frequency bands using an analysis bank of
M
filters of
bandwidth
π/
M
. The signal in any of these
M
channels is then downsampled by a factor
L
.
