Databases Reference
In-Depth Information
T A B L E 14 . 5
Coefficients for the 16-tap
Smith-Barnwell low-pass
filter.
h
0
0
.
02193598203004352
h
1
0
.
001578616497663704
h
2
−
0
.
06025449102875281
h
3
−
0
.
0118906596205391
0
.
137537915636625
h
4
.
h
5
0
05745450056390939
−
.
h
6
0
321670296165893
h
7
−
0
.
528720271545339
h
8
−
0
.
295779674500919
h
9
0
.
0002043110845170894
h
10
0
.
02906699789446796
h
11
−
0
.
03533486088708146
h
12
−
0
.
006821045322743358
h
13
0
.
02606678468264118
h
14
0
.
001033363491944126
h
15
−
0
.
01435930957477529
14.4 The Basic Subband Coding Algorithm
The basic subband coding system is shown in Figure
14.7
.
14.4.1 Analysis
The source output is passed through a bank of filters, called the analysis filter bank, which
covers the range of frequencies that make up the source output. The passbands of the filters can
be nonoverlapping or overlapping. Nonoverlapping and overlapping filter banks are shown in
Figure
14.8
. The outputs of the filters are then subsampled.
The justification for the subsampling is the Nyquist rule and its generalization, which tells
us that we only need twice as many samples per second as the range of frequencies. This
means that we can reduce the number of samples at the output of the filter because the range
of frequencies at the output of the filter is less than the range of frequencies at the input to the
filter. This process of reducing the number of samples is called
decimation
,
1
or
downsampling
.
The amount of decimation depends on the ratio of the bandwidth of the filter output to the
filter input. If the bandwidth at the output of the filter is 1
M
of the bandwidth at the input to
the filter, we would decimate the output by a factor of
M
by keeping every
M
th sample. The
symbol
M
/
↓
is used to denote this decimation.
1
The word
decimation
has a rather bloody origin. During the time of the Roman empire, if a legion broke
ranks and ran during battle, its members were lined up and every tenth person was killed. This process was called
decimation.
