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174
Baseband Pulse and Digital Signaling Chap. 3
Substituting this and Eq. (3–40) into Eq. (3–36a), the PSD for Manchester NRZ becomes
Manchester NRZ (f) = A 2 T b a sin (pfT 2
b/2)
b sin 2 (pfT (3–46c)
pfT b /2
b /2)
where A = 1 if the normalized average power is unity.
This spectrum is plotted in Fig. 3–16e. The null bandwidth of the Manchester format is
twice that of the bipolar bandwidth. However, the Manchester code has a Zero DC level on a
bit-by-bit basis. Moreover, a string of zeros will not cause a loss of the clocking signal.
In reviewing our study of PSD for digital signals, it should be emphasized that the spectrum
is a function of the bit pattern (via the bit autocorrelation) as well as the pulse shape. The
general result for the PSD, Eq. (3–36), is valid for multilevel as well as binary signaling.
Differential Coding
When serial data are passed through many circuits along a communication channel, the waveform
is often unintentionally inverted (i.e., data complemented). This result can occur in a
twisted-pair transmission line channel just by switching the two leads at a connection point
when a polar line code is used. (Note that such switching would not affect the data on a bipolar
signal.) To ameliorate the problem, differential coding, as illustrated in Fig. 3–17, is often
employed. The encoded differential data are generated by
e n = d n e n-1
(3–47)
Data in
Differential encoder
d n
modulo 2 adder
e n
Line encoder
circuit
Delay
T b
Channel
Line decoder
circuit
e n – 1
Delay
T b ~ e n – 1
Differential decoder
~ e n
modulo 2 adder
~
d n
Data out
Figure 3–17
Differential coding system.