Databases Reference
In-Depth Information
3
2
1
0
−
1
−2
−3
500
1000
1500
2000
2500
3000
3500
4000
F I GU R E 11 . 10
The reconstructed sequence using a third-order predictor and an
eight-level Jayant quantizer.
DPCM with Forward Adaptive Prediction (DPCM-APF)
In forward adaptive prediction, the input is divided into segments or blocks. In speech coding
this block usually consists of about 16ms of speech. At a sampling rate of 8000 samples per
second, this corresponds to 128 samples per block [
134
,
172
]. In image coding, we use an
8
8 block [
173
].
The autocorrelation coefficients are computed for each block. The predictor coefficients
are obtained from the autocorrelation coefficients and quantized using a relatively high-rate
quantizer. If the coefficient values are to be quantized directly, we need to use at least 12
bits per coefficient [
134
]. This number can be reduced considerably if we represent the
predictor coefficients in terms of
parcor coefficients
; we will describe how to obtain the parcor
coefficients in Chapter 17. For now, let's assume that the coefficients can be transmitted with
an expenditure of about 6 bits per coefficient.
In order to estimate the autocorrelation for each block, we generally assume that the sample
values outside each block are zero. Therefore, for a block length of
M
, the autocorrelation
function for the
l
th block would be estimated by
×
lM
−
k
1
R
(
l
)
xx
(
k
)
=
x
i
x
i
+
k
(38)
M
−
k
i
=
(
l
−
1
)
M
+
1
for
k
positive, or
lM
1
R
(
l
)
xx
(
k
)
=
x
i
x
i
+
k
(39)
M
+
k
i
=
(
l
−
1
)
M
+
1
−
k
for
k
negative. Notice that
R
(
l
)
R
(
l
)
(
k
)
=
(
−
k
)
, which agrees with our initial assumption.
xx
xx
