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Unformatted text preview: ion on (4.4) reviews that it is possible to have no ISI even if the Ú ´Øµ is bandlimited,
i.e., the basic pulse shape Ù´Øµ and/or the channel is bandlimited. More precisely, letting Ü´Øµ Ú £Ú´Øµ, we can rewrite the decision statistic ÞÑ in (4.4) as: ÞÑ Ñ Ü´¼µ · ÒÑ Ò Ü´ÑÌ ÒÌ µ · ÒÑ (4.5) There is no ISI if the Nyquist condition is satisﬁed: Ò
for Ü´ÒÌ µ ¼ ¼
¼ where is some constant and, without loss of generality, we can set (4.6) ½. The Nyquist condition in this form is not very helpful in the design of ISI-free pulses. It turns out that it is more illustrative to
restate the Nyquist condition in frequency domain. To do so, ﬁrst let ÜÆ ´Øµ ½
Ò ½ Ü´ÒÌ µÆ ´Ø ÒÌ µ
4.4 (4.7) Wong & Lok: Theory of Digital Communications ½
Figure 4.3: Case Ì 4. ISI & Equalization ¾Ï : non-overlapping spectrum Taking Fourier transform, ½ ½ Æ´ µ Ò Ì (4.8) Ì (4.9) Ì Ò ½
where ´ µ is the Fourier transform of...
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- Spring '08