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Unformatted text preview: Ìµ (4.11) Wong & Lok: Theory of Digital Communications 4. ISI & Equalization ½
Figure 4.4: Case Ì ¾Ï : overlapping spectrum We note that the sinc pulse is not timelimited and is not causal. Therefore, it is not physically ½
realizable. A truncated and delayed version is used as an approximation. The critical rate Ì ¾Ï above which ISI is unavoidable is known as the Nyquist rate. ¯ ½
Suppose that the symbol rate is even slower so that Ì
their neighbors. The folded spectrum
of È½ Ò ½ ¾Ï . Then, copies of ´ µ overlap with
´ Ì µ can be ﬂat with many different choices ´ µ. An example is shown in Figure 4.4. Therefore, we can design an ISI-free pulse shape which gives a ﬂat folded spectrum.
When the symbol rate is below the Nyquist rate, a widely used ISI-free spectrum is the raised-cosine
spectrum (Figure 4.5): ´µ Ì
Ì ¾ ¼ for ½ · Ó× «Ì ´ ½¾ « µ
Ì for ¼ ½ «
¾Ì for ½·«
¾Ì ½ «
¾Ì (4.12) It determines the excess b...
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- Spring '08