Databases Reference
In-Depth Information
Example14.2.1:
{
x
n
}
Suppose we want to encode the following sequence of values
:
10
14
10
12
14
8
14
12
10
8
10
12
There is a significant amount of sample-to-sample correlation, so we might consider using a
DPCM scheme to compress this sequence. In order to get an idea of the requirements on the
quantizer in a DPCM scheme, let us take a look at the sample-to-sample differences
x
n
−
x
n
−
1
:
10
4
−
422
−
66
−
2
−
2
−
222
Ignoring the first value, the dynamic range of the differences is from
6 to 6. Suppose we
want to quantize these values using
m
bits per sample. This means we could use a quantizer
with
M
−
2
m
levels or reconstruction values. If we choose a uniform quantizer, the size of
each quantization interval,
=
, is the range of possible input values divided by the total number
of reconstruction values. Therefore,
12
M
=
2
6
which would give us a maximum quantization error of
or
M
.
according to (
1
) and (
2
). All three
sequences are plotted in Figure
14.2
. Notice that given
y
n
and
z
n
, we can always recover
x
n
:
Now let's generate two new sequences
{
y
n
}
and
{
z
n
}
x
n
=
y
n
+
z
n
(3)
+
+
+
+
+
+
14
14
+
+
x
n
x
n
y
n
y
n
+
+
12
12
+
+
+
+
z
n
z
n
10
10
+
+
+
+
+
+
+
+
+
+
+
+
8
8
6
6
Value
Value
4
4
2
0
2
0
Sample
number
Sample
number
2
2
4
4
6
6
12
12
8
8
10
10
−
2
4
2
4
−
F I GU R E 14 . 2
Original set of samples and the two components.
