4
Binary (digital) data transmission
In modern communications, it it increasingly common to transmit digital rather than analog
data. In their simplest form, digital transmissions encode everything as binary 1’s or 0’s,
rather than the continuous signal range possible with an analog broadcast. Obvious examples
are internet communications, digital cable / satellite , and digital cell phone service. As an
example, the decimal number 89 is represented in binary as ‘01011001’. This could represent
a decimal number, the ASCII character ‘y’, or a sampled voltage level determined by an
analog to digital converter. We can represent this digital data by a message signal
m
(
t
) as
shown in Fig. 94 This message would be generated, for example, by a computer serial port
t
A

A
)
(
t
m
0
1
0
0
0
0
1
1
1
b
T
Figure 94:
or USB port.
The amount of time occupied by each bit is called the bit period
T
b
. Intuitively, we know
that the smaller the bit period, the faster we are transmitting data. We can also describe the
transmission speed by the bit rate,
R
usually in bits per second. The bit rate is of course the
reciprocal of the bit period. Faster data transmission implies increased bandwidth, giving
us the empirical relation
bandwidth
∝
R
=
1
T
b
.
(69)
Transmitting this digital signal is no different than transmitting any other message. We
want to shift it in frequency so that it occupies a unique frequency band where it will not
interfere with messages being transmitted over the same channel. We already know how to
modulate and demodulate this message using either AM or FM techniques; what follows can
be thought of simply as more examples of these modulation schemes.
4.1
Digital DSBSC Modulation (BPSK)
We can start by writing the digital message mathematically as
m
(
t
) =
A
∞
summationdisplay
n
=0
b
n
Π
parenleftbigg
t

nT
b
T
b
parenrightbigg
(70)
87
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The coefficients
b
n
represent either +1 for a ‘1’ or 1 for a ‘0’. These multiply a rectangular
pulse function
Π
parenleftbigg
t
T
b
parenrightbigg
=
p
(
t
)
with a width of
T
b
(one bit period) shifted over by
nT
b
. The important thing here is that
each bit in the binary data stream results in a rectangular pulse
p
(
t
) with a width of
T
b
.
We can modulate this message using DSBSC modulation in the same way as was de
scribed in section 2.3.
A block diagram of the procedure is reproduced in Fig. 95.
The
)
2
cos(
)
(
t
f
t
c
TX
p
=
l
)
(
t
m
)
(
t
s
Figure 95:
message is modulated with a cosine at the carrier frequency which shifts its spectrum up
and down by
f
c
. This gives
s
(
t
) =
m
(
t
) cos(2
πf
c
t
)
.
The simplicity of the message (either
±
A
) allows us to write
s
(
t
) =
braceleftbigg
A
cos(2
πf
c
t
)
,
b
n
= +1

A
cos(2
πf
c
t
)
,
b
n
=

1
or
s
(
t
) =
braceleftbigg
A
cos(2
πf
c
t
)
,
b
n
= +1
A
cos(2
πf
c
t
±
π
)
,
b
n
=

1
(71)
The second form shows that in the DSBSC modulated message, a binary ‘1’ and ‘0’ are
differentiated by a phase shift of 180
◦
(
π
) in the transmitted signal. The actual frequency
remains the same. For this reason, DSBSC applied to a digital signal is commonly called
Binary Phase Shift Keying (BPSK). This is a change in name only. Analysis of BPSK in the
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 Summer '09
 Osama
 BPSK, bit period

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