Digital Signal Processing Reference
In-Depth Information
So,
m
q
[
k
]
=
m
q
[
k
−
2]
+
d
q
[
k
−
1]
+
d
q
[
k
]
(2.40)
Proceeding iteratively in this manner and considering 0 initial condition, i.e.
k
m
q
[0]
=
0, we have
m
q
[
k
]
=
d
q
[
n
]
(2.41)
n
=
0
This shows that the receiver is just an accumulator. If the output
d
q
[
k
] is repre-
sented by impulses, then the accumulator (receiver) may be realized by an integrator
because its output is the sum of the strengths of input impulses (sum of the areas
under the impulses). We may replace the feedback portion of the modulator (which
is identical to the demodulator) by an integrator. The demodulator output is
m
q
[
k
],
which when passed through an LPF gives us the retrieved signal. The Fig.
2.26
bellows shows a practical implementation of the delta modulator and demodulator.
Comparator
Sampler frequency
f
s
m(t)
E
∑
d
q
(
t
)
-
-
E
^
m
q
(
t
)
∫
Integrator
(a)
m
(
t
)
^
m
q
(
t
)
d
q
[
k
]
∫
Low pass filter
(b)
~
m
(
t
)
m
(
t
)
t
P
i
(
t
)
t
Fig. 2.26
(
a
)Delta
modulator, (
b
)Delta
demodulator, (
c
)DM
waveforms
P
o
(
t
)
t
(c)
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