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Sec. 3–6 Intersymbol Interference 185
TABLE 3–6
Code Type
SPECTRAL EFFICIENCIES OF LINE CODES
First Null Bandwidth
(Hz)
Spectral Efficiency
h = RB [(bits/s)/Hz]
Unipolar NRZ R 1
Polar NRZ R 1
1
Unipolar RZ
2R
2
Bipolar RZ R 1
1
Manchester NRZ
2R
2
Multilevel polar NRZ R
All of these binary line codes have h ≤ 1. Multilevel signaling can be used to achieve
much greater spectral efficiency, but multilevel circuits are more costly. In practice, multilevel
polar NRZ signaling is used in the T1G digital telephone lines, as described in Sec. 3–9.
3–6 INTERSYMBOL INTERFERENCE
The absolute bandwidth of rectangular multilevel pulses is infinity. If these pulses are filtered
improperly as they pass through a communication system, they will spread in time, and the
pulse for each symbol may be smeared into adjacent time slots and cause intersymbol interference
(ISI), as illustrated in Fig. 3–23. Now, how can we restrict the bandwidth and still not
introduce ISI? Of course, with a restricted bandwidth, the pulses would have rounded tops
(instead of flat ones). This problem was first studied by Nyquist [1928]. He discovered three
different methods for pulse shaping that could be used to eliminate ISI. Each of these methods
will be studied in the sections that follow.
Input waveform, w in (t)
1 0 0 0
Individual pulse response
Received waveform, w out (t)
(sum of pulse responses)
0
t
0
t
0
t
1 0 1 1
T s
T s T s
Intersymbol interference
0 t 0 t 0
t
Sampling points
(transmitter clock)
Sampling points
(receiver clock)
Sampling points
(receiver clock)
Figure 3–23
Examples of ISI on received pulses in a binary communication system.