Digital Signal Processing Reference
In-Depth Information
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TX
I
(
t
)
s
(
t
)
F
s
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,
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Figure 12.3
Abstract view of a digital transmitter.
as shown in Figure 12.3. Here, we neglect the details associated to the dig-
ital modulation process and concentrate on the digital-to-analog interface,
represented in the picture by the interpolator
I
; the input to the trans-
mitter is some generic binary data, represented as a bit stream. The band-
width constraints imposed by the channel can be represented graphically
as in Figure 12.4. In order to produce a signal which “sits” in the prescribed
frequency band, we need to use a D
(
t
)
/
A converter working at a frequency
F
s
2
f
max
. Once the interpolation frequency is chosen (and we will see
momentarily the criteria to do so), the requirements for the discrete-time
signal
s
≥
[
n
]
are set. The bandwidth requirements become simply
f
min,max
F
s
and they can be represented as in Figure 12.5 (in the figure, for instance, we
have chosen
F
s
ω
=
2
π
min,max
=
2.28
f
max
).
bandwidth constraint
power constraint
0
f
min
f
max
F
s
F
Figure 12.4
Analog specifications (positive frequencies) for the transmitter.
by looking
more in detail into the input side of the transmitter, as shown in Figure 12.6.
The input bitstream is first processed by a
scrambler
,whosepurposeisto
randomize the data; clearly, it is a pseudo-randomization since this opera-
tion needs to be undone algorithmically at the receiver. Please note how the
implementation of the transmitter in the digital domain allows for a seam-
less integration between the transmission scheme and more abstract data
We can now try to understand how to build a suitable
s
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