Databases Reference
In-Depth Information
Output
3.5
2.5
1.5
0.5
−
4.0
−
3.0
−
2.0
−
1.0
1.0
2.0
3.0
4.0
Input
−0.5
−1.5
−2.5
−3.5
F I GU R E 9 . 3
Quantizer input-output map.
Construction of the intervals (their location, etc.) can be viewed as part of the design of
the encoder. Selection of reconstruction values is part of the design of the decoder. However,
the fidelity of the reconstruction depends on both the intervals and the reconstruction values.
Therefore, when designing or analyzing encoders and decoders, it is reasonable to view them
as a pair. We call this encoder-decoder pair a
quantizer
. The quantizer mapping for the 3-bit
encoder-decoder pair shown in Figures
9.1
and
9.2
can be represented by the input-output map
shown in Figure
9.3
. The quantizer accepts sample values, and depending on the interval in
which the sample values fall, it provides an output codeword and a representation value. Using
the map of Figure
9.3
, we can see that an input to the quantizer of 1.7 will result in an output
of 1.5, and an input of
5.
From Figures
9.1
,
9.2
,
9.3
we can see that we need to know how to divide the input range
into intervals, assign binary codes to these intervals, and find representation or output values
for these intervals in order to specify a quantizer. We need to do all of this while satisfying
distortion and rate criteria. In this chapter, we will define distortion to be the average squared
difference between the quantizer input and output. We call this the mean squared quantization
error (
msqe
) and denote it by
−
0
.
3 will result in an output of
−
0
.
2
σ
q
. The rate of the quantizer is the average number of bits
