Databases Reference
In-Depth Information
6
+
x
n
−
x
n
−1
y
n
−
y
n
−1
+
4
+
+
2
+
Sample
number
Value
0
2
4
6
8
10
12
+
+
−
2
+
−
4
+
−
6
F I GU R E 14 . 3
Difference sequences generated from the original and averaged se-
quences.
Let's try to encode each of these sequences. The sequence
{
y
n
}
is
10
12
12
11
13
11
11
13
11
10
9
11
Notice that the
sequence—the sample-to-sample
variation is much smaller. This becomes evident when we look at the sample-to-sample
differences:
{
y
n
}
sequence is “smoother” than the
{
x
n
}
020
−
12
−
202
−
2
−
1
−
12
The difference sequences
areplottedinFigure
14.3
.Again,
ignoring the first difference, the dynamic range of the differences
y
n
−
{
x
n
−
x
n
−
1
}
and
{
y
n
−
y
n
−
1
}
y
n
−
1
is 4. If we take
the dynamic range of these differences as a measure of the range of the quantizer, then for an
M
-level quantizer, the step size of the quantizer is
4
2
M
.
This maximum quantization error is one-third the maximum quantization error incurred when
the
M
and the maximumquantization error is
{
x
n
}
sequence is quantized using an
M
-level quantizer. However, in order to reconstruct
{
x
n
}
, we also need to transmit
{
z
n
}
.The
{
z
n
}
sequence is
