Databases Reference
In-Depth Information
Quantizer
output
x
2
3Δ
2Δ
Δ
−3Δ−
2Δ
−Δ
Δ
2Δ
3Δ
x
1
−Δ
−2Δ
−
3
Δ
F I GU R E 10 . 5
Input-output map for consecutive quantization of two inputs using
an eight-level scalar quantizer.
squared value of the source output samples and the mean squared error. As the average squared
value of the source output is the same in both cases, an increase in SNR means a decrease
in the mean squared error. Whether this increase in SNR is significant will depend on the
particular application. What is important here is that by treating the source output in groups
of two we could effect a positive change with only a minor modification. We could argue
that this modification is really not that minor since the uniform characteristic of the original
quantizer has been destroyed. However, if we begin with a nonuniform quantizer and modify
it in a similar way, we get similar results.
Could we do something similar with the scalar quantizer? If we move the output point at
2
to the origin, the SNR
drops
from 11.44 dB to 10.8 dB. What is it that permits us to make
modifications in the vector case, but not in the scalar case? This advantage is caused by the
added flexibility we get by viewing the quantization process in higher dimensions. Consider
the effect of moving the output point from
7
2
to the origin in terms of two consecutive inputs.
This one change in one dimension corresponds to moving 15 output points in two dimensions.
Thus, modifications at the scalar quantizer level are gross modifications when viewed from
7
