Databases Reference
In-Depth Information
Output
7
Δ
/2
5
Δ
/2
3
Δ
/2
Δ
/2
−
3
Δ−
2
Δ
−Δ
Δ
2
Δ
3
Δ
Input
-
Δ
/2
−
3
Δ
/2
−
5
Δ
/2
−
7
Δ
/2
F I GU R E 9 . 16
Output levels for the Jayant quantizer.
The expansion and contraction of the step size is accomplished in the Jayant quantizer by
assigning a
multiplier M
k
to each interval. If the
th input falls in the
k
th interval, the step
size to be used for the
n
th input is obtained by multiplying the step size used for the
(
n
−
1
)
th
input with
M
k
. The multiplier values for the inner levels in the quantizer are less than one, and
the multiplier values for the outer levels of the quantizer are greater than one. Therefore, if an
input falls into the inner levels, the quantizer used to quantize the next input will have a smaller
step size. Similarly, if an input falls into the outer levels, the step size will be multiplied with
a value greater than one, and the next input will be quantized using a larger step size. Notice
that the step size for the current input is modified based on the previous quantizer output. The
previous quantizer output is available to both the transmitter and receiver, so there is no need to
send any additional information to inform the receiver about the adaptation. Mathematically,
the adaptation process can be represented as
(
n
−
1
)
n
=
M
l
(
n
−
1
)
n
−
1
(21)
where
l
1.
In Figure
9.16
we show a 3-bit uniform quantizer. We have eight intervals represented by
the different quantizer outputs. However, the multipliers for symmetric intervals are identical
(
n
−
1
)
is the quantization interval at time
n
−
