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Sec. 3–5 Line Codes and Spectra 167
• Transmission bandwidth. This should be as small as possible.
• Error detection capability. It should be possible to implement this feature easily by the
addition of channel encoders and decoders, or the feature should be incorporated into
the line code.
• Transparency. The data protocol and line code are designed so that every possible
sequence of data is faithfully and transparently received.
A protocol is not transparent if certain words are reserved for control sequences so that,
for example, a certain word instructs the receiver to send all data that follow that code word to
the printer. This feature causes a problem when a random data file (such as a machine language
file) is transferred over the link, since some of the words in the file might be control
character sequences. These sequences would be intercepted by the receiving system, and the
defined action would be carried out, instead of passing the word on to the intended destination.
In addition, a code is not transparent if some sequence will result in a loss of clocking
signal (out of the bit synchronizer at the receiver). Because a string of zeros will result in a
loss of the clocking signal, the bipolar format is not transparent.
The particular type of waveform selected for digital signaling depends on the application.
The advantages and disadvantages of each signal format are discussed further after their
spectra have been derived.
Power Spectra for Binary Line Codes
The PSD can be evaluated by using either a deterministic or a stochastic technique. This was
first discussed in Chapter 1 and later illustrated in Example 2–22. To evaluate the PSD using
the deterministic technique, the waveform for a line code that results from a particular data
sequence is used. The approximate PSD is then evaluated by using Eq. (2–66) or, if the line
code is periodic, Eq. (2–126). (Work Prob. 3–24 to apply this deterministic approach.)
Alternatively, the PSD may be evaluated by using the stochastic approach that is developed in
Chapter 6. The stochastic approach will be used to obtain the PSD of line codes that are
shown in Fig. 3–15, because it gives the PSD for the line code with a random data sequence
(instead of that for a particular data sequence).
As discussed and illustrated in Section 3–4, a digital signal (or line code) can be represented
by
q
s(t) = a a n f(t - nT s )
(3–35)
n=-q
where f(t) is the symbol pulse shape and T s is the duration of one symbol. For binary signaling,
T s = T b , where T b is the time that it takes to send 1 bit. For multilevel signaling,
T s = T b . The set {a n } is the set of random data. For example, for the unipolar NRZ line
code, f(t) =ßA t T b
B and a n =+A V when a binary 1 is sent and a n = 0 V when a binary 0
is sent.
As is proven in Sec. 6–2, from Eq. (6–70), the general expression for the PSD of a digital
signal is
s (f) = |F(f)|2
T s
q
a R(k)e j2pkfT s
k=-q
(3–36a)