Databases Reference
In-Depth Information
We can see that the basic subband system is simple. The three major components of
this system are the
analysis and synthesis filters
,the
bit allocation
scheme, and the
encoding
scheme. A substantial amount of research has focused on each of these components. Various
filter bank structures have been studied in order to find filters that are simple to implement and
provide good separation between the frequency bands. In the next section we briefly look at
some of the techniques used in the design of filter banks, but our descriptions are necessarily
limited. For a (much) more detailed look, see the excellent topic by P.P. Vaidyanathan [
206
].
The bit allocation procedures have also been extensively studied in the contexts of subband
coding, wavelet-based coding, and transform coding. We have already described some bit
allocation schemes in Section 13.5, and we describe a different approach in Section
14.9
.
There are also some bit allocation procedures that have been developed in the context of
wavelets, which we describe in the next chapter.
The separation of the source output according to frequency also opens up the possibility
for innovative ways to use compression algorithms. The decomposition of the source output
in this manner provides inputs for the compression algorithms, each of which has more clearly
defined characteristics than the original source output. We can use these characteristics to
select separate compression schemes appropriate to each of the different inputs.
Human perception of audio and video inputs is frequency dependent. We can use this
fact to design our compression schemes so that the frequency bands that are most important to
perception are reconstructed most accurately. Whatever distortion there has to be is introduced
in the frequency bands to which humans are least sensitive. We describe some applications to
the coding of speech, audio, and images later in this chapter.
Before we proceed to bit allocation procedures and implementations, we provide a more
mathematical analysis of the subband coding system. We also look at some approaches to
the design of filter banks for subband coding. The analysis relies heavily on the Z-transform
concepts introduced in Chapter 11 and will primarily be of interest to readers with an electrical
engineering background. The material is not essential to understanding the rest of the chapter;
if you are not interested in these details, you should skip these sections and go directly to
Section
14.9
.
14.5 Design of Filter Banks
In this section we will take a closer look at the analysis, downsampling, upsampling, and
synthesis operations. Our approach follows that of [
207
]. We assume familiarity with the
Z-transform concepts of Chapter 12. We begin with some notation. Suppose we have a
sequence
x
0
,
x
1
,
x
2
,...
. We can divide this sequence into two subsequences:
x
0
,
x
2
,
x
4
,...
using the scheme shown in Figure
14.9
, where
z
−
1
corresponds to a delay
and
x
1
,
x
3
,
x
5
,...
of one sample and
M
denotes a subsampling by a factor of
M
. This subsampling process is
called
downsampling
or
decimation
.
The original sequence can be recovered from the two downsampled sequences by inserting
0s between consecutive samples of the subsequences, delaying the top branch by one sample
and adding the two together. Adding 0s between consecutive samples is called
upsampling
and is denoted by
↓
↑
M
. The reconstruction process is shown in Figure
14.10
.
