Databases Reference
In-Depth Information
T A B L E 9 . 5
Operation of a Jayant quantizer.
n
n
Input
Output Level
Output
Error
Update Equation
0
0.5
0.1
0
0
.
25
0
.
15
1
=
M
0
×
0
1
0.4
−
0.2
4
−
0
.
2
0
.
0
2
=
M
4
×
1
2
0.32
0.2
0
0
.
16
0
.
04
3
=
M
0
×
2
3
0.256
0.1
0
0
.
128
0
.
028
4
=
M
0
×
3
4
0.2048
−
0.3
5
−
0
.
3072
−
0
.
0072
5
=
M
5
×
4
5
0.1843
0.1
0
0
.
0922
−
0
.
0078
6
=
M
0
×
5
6
0.1475
0.2
1
0
.
2212
0
.
0212
7
=
M
1
×
6
7
0.1328
0.5
3
0
.
4646
−
0
.
0354
8
=
M
3
×
7
8
0.1594
0.9
3
0
.
5578
−
0
.
3422
9
=
M
3
×
8
9
0.1913
1.5
3
0
.
6696
−
0
.
8304
10
=
M
3
×
9
10
0.2296
1.0
3
0
.
8036
0
.
1964
11
=
M
3
×
10
11
0.2755
0.9
3
0
.
9643
0
.
0643
12
=
M
3
×
11
because of symmetry:
M
0
=
M
4
M
1
=
M
5
M
2
=
M
6
M
3
=
M
7
Therefore, we only need four multipliers. To see how the adaptation proceeds, let us work
through a simple example using this quantizer.
Example9.5.3: Jayant Quantizer
For the quantizer in Figure
9.16
, suppose the multiplier values are
M
0
=
M
4
=
0
.
8
,
M
1
=
=
.
,
=
=
,
=
=
.
0
,is
M
5
0
9
M
2
M
6
1
and
M
3
M
7
1
2; the initial value of the step size,
.
,
−
.
,
.
,
.
,
−
.
,
.
,
.
,
.
,
.
,
.
,...
0.5; and the sequence to be quantized is 0
.
When the first input is received, the quantizer step size is 0.5. Therefore, the input falls into
level 0, and the output value is 0.25, resulting in an error of 0.15. As this input fell into
quantizer level 0, the new step size
1
0
2
0
2
0
1
0
3
0
1
0
2
0
5
0
9
1
5
1
is
M
0
×
0
=
0
.
8
×
0
.
5
=
0
.
4. The next input is
−
0
.
2,
which falls into level 4. As the step size at this time is 0.4, the output is
2. To update, we
multiply the current step size with
M
4
. Continuing in this fashion, we get the sequence of step
sizes and outputs shown in Table
9.5
.
Notice how the quantizer adapts to the input. In the beginning of the sequence, the input
values are mostly small, and the quantizer step size becomes progressively smaller, providing
better and better estimates of the input. At the end of the sample sequence, the input values are
large, and the step size becomes progressively bigger. However, the size of the error is quite
large during the transition. This means that if the input was changing rapidly, which would
happen if we had a high-frequency input, such transition situations would be much more likely
to occur, and the quantizer would not function very well. However, in cases where the statistics
of the input change slowly, the quantizer could adapt to the input. As most natural sources
such as speech and images tend to be correlated, their values do not change drastically from
sample to sample. Even when some of this structure is removed through some transformation,
the residual structure is generally enough for the Jayant quantizer (or some variation of it) to
function quite effectively.
−
0
.
