Databases Reference
In-Depth Information
Weight (lb)
215
190
165
140
115
90
65
40
Height (in)
40
50
60
70
F I GU R E 10 . 3
The height-weight vector quantizer when height and weight are
taken to be components of a vector.
Example10.3.2:
Suppose we have to design a uniform quantizer with eight output values for a Laplacian input.
Using the information from Table 9.3 in Chapter 9, we would obtain the quantizer shown
in Figure
10.4
, where
is equal to 0.7309. As the input has a Laplacian distribution, the
probability of the source output falling in the different quantization intervals is not the same.
For example, the probability that the input will fall in the interval
[
0
,)
is 0.3242, while the
probability that a source output will fall in the interval
is 0.0225. Let's look at how
this quantizer will quantize two consecutive source outputs. As we did in the previous example,
let's plot the first sample along the
x
-axis and the second sample along the
y
-axis. We can
represent this two-dimensional view of the quantization process as shown in Figure
10.5
.Note
that, as in the previous example, we have not changed the quantization process; we are simply
representing it differently. The first quantizer input, which we have represented in the figure
as
x
1
, is quantized to the same eight possible output values as before. The same is true for the
second quantizer input, which we have represented in the figure as
x
2
. This two-dimensional
representation allows us to examine the quantization process in a slightly different manner.
[
3
,
∞
)
