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172
Baseband Pulse and Digital Signaling Chap. 3
For k = 1 (the adjacent-bit case) and the data sequences (1, 1), (1, 0), (0, 1), and (0, 0),
the possible a n a n + 1 products are -A 2 , 0, 0, and 0. Each of these sequences occurs with a probability
of Consequently,
1
4 .
R(1) = a
4
i=1
(a n a n+1 ) i P i =- A2
4
For k 7 1, the bits being considered are not adjacent, and the a n a n + k products are ;A 2 ,
1
0, 0, and 0; these occur with a probability of Then
R(k 7 1) = a
5
i=1
4 .
(a n a n+k ) i P i = A 2 # 1 8 - A2 # 1 8 = 0
Thus,
R bipolar (k) = f
A 2
2 , k = 0
- A2
4 , |k| = 1 v
0, |k| 7 1
(3–44)
Example 3–9 PSD FOR A BIPOLAR RZ LINE CODE USING THE DATA
AUTOCORRELATION
Evaluate and plot the PSD for a bipolar RZ line code with R = 1. For the solution, use Eqs.
(3–36a) and (3–44). See Example3_09.m. Compare this result with Fig. 3–16d.
Using Eqs. (3–44) and (3–42) in Eq. (3–36a), where T s = T b , we find that the PSD for the
bipolar RZ line code is
or
bipolar RZ (f) = A2 T b
8
bipolar RZ(f) = A2 T b
4
a sin (pfT 2
b>2
b (1 - cos (2pfT
pfT b >2
b ))
a sin (pfT b>2
pfT b >2 b 2
sin 2 (pfT b )
(3–45)
where A = 2 if the normalized average power is unity. This PSD is plotted in Fig. 3–16d.
Bipolar signaling has a spectral null at DC, so AC–coupled circuits may be used in the transmission
path.