When the symbol rate is below the nyquist rate a

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Unformatted text preview: ̵ (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 Ƚ Ò ½ ¾Ï . Then, copies of ´ µ overlap with Ò ´ 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 ½·« ¾Ì (4.12) It determines the excess b...
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