6 the nyquist condition in this form is not very

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ٴص and/or the channel is bandlimited. More precisely, letting ܴص 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 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...
View Full Document

Ask a homework question - tutors are online