Databases Reference
In-Depth Information
x
−
Q(x)
Overload noise
Δ/2
−4Δ
3Δ 2Δ−Δ
Δ
2Δ
3Δ
4Δ
x
−Δ/2
Granular noise
F I GU R E 9 . 9
Quantization error for a uniform midrise quantizer.
Granular probability
2Δ
−4Δ−3Δ−2Δ−Δ
Δ
3Δ
4Δ
x
Overload probability
F I GU R E 9 . 10
Overload and granular regions for a 3-bit uniform quantizer.
the overload noise. The probability that the input will fall into the overload region is called
the
overload probability
(Figure
9.10
).
The nonuniform sources we deal with have probability density functions that are generally
peaked at zero and decay as we move away from the origin. Therefore, the overload probability
is generally much smaller than the probability of the input falling in the granular region. As we
see from Equation (
19
), an increase in the step size
will result in an increase in the value of
2
1
, which in turn will result in a decrease in the overload probability and the second
term in Equation (
19
). However, an increase in the step size
−
will also increase the granular
