Digital Signal Processing Reference
In-Depth Information
This shows that
m
q
[
k
] is a quantized form of
m
[
k
]. The predictor input is indeed
m
q
[
k
] as assumed.
The receiver shown in Fig.
2.24
is identical to the shaded portion of the transmit-
ter. The inputs in both cases are also the same
d
q
[
k
]. The predictor output must be
m
q
[
k
].
2.4 Delta Modulation
Sample correlation used in DPCM is further explained in Delta Modulation (DM)
by over sampling (typically 4 times the Nyquist rate) the baseband signal. This
increases the correlation between adjacent samples, which results in a small pre-
diction error that can be encoded using only one bit (no. of levels
2). Thus DM
is basically a one bit DPCM, that is, a DPCM that uses only two levels (L
=
=
2) for
quantization of the
m
[
k
]
−ˆ
m
q
[
k
]. For more simple scheme the difference between
m
[
k
] and
m
[
k
1] is encoded by only one bit. That is if
m
[
k
] is higher than
m
[
k
]
then 1 is transmitted, otherwise 0.
In comparison to PCM (and also DPCM), it is very simple method of A/D con-
version. In DM the word framing is unnecessary in transmitter and receiver. This
strategy allows us to use fewer bits per sample for encoding a base band signal.
In delta modulation, we use a first order predictor, which, as seen earlier, is just
a time delay of
T
S
. Thus the DPCM transmitter and receiver can be reconfigured to
delta modulation as shown in the following Fig.
2.25
.
−
d
q
[
k
]
Fig. 2.25
Delta modulation
as a special case of DPCM
m[k]
∑
Quantizer
m
q
[
k
−1]
∑
Delay
T
S
m
q
[
k
]
Accumulator
Here
m
q
[
k
]
=
m
q
[
k
−
1]
+
d
q
[
k
]
Hence,
m
q
[
k
−
1]
=
m
q
[
k
−
2]
+
d
q
[
k
−
1]
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