dc

e
n mn
mˆ
n
is
a
mˆ
n
The quantizer output is
e
q
n en
qn
qnis
where
The prediction filter input is
m
q
n mˆ
n
en qn
m
q
Processing Gain:
2
where
2
where
prediction
From (3.74)
The (SNR)
(SNR)
M
(SNR)
E
(SNR)
Processing Gain,
value.
(3.74)
(3.75)
quantizati on error.
(3.77)
mn
n mn
qn (3.78)
of the DPCM systemis
2
and
o
o
o
2
M
2
Q
2
M
(
2
G
2
E
)( )
2
(SNR)
G
(3.79)
(3.80)
Design a prediction filter to maximize
is the variance of the predictions error
and the signal - to - quantizati on noise ratio is
Q
p
Q
are variances of m n
E
2
E
2
Q
p
Q
Q
(3.81)
(3.82)
2
M
2
E
( E[
m[
n]]
0) and q
G
p
2
(minimize )
E
n