Unformatted text preview: Ü´Øµ. The Nyquist condition in (4.6) is equivalent to the
condition ÜÆ ´Øµ Æ ´Øµ or Æ ´ µ ½ in frequency domain. Now, by employing (4.8), we get
½
Ò Ò Ì ½ This is the equivalent Nyquist condition in frequency domain. It says that the folded spectrum of Ü´Øµ
has to be ﬂat for not having ISI. ´ µ ¼ for When the channel is bandlimited to Ï Hz, i.e., Ï , the Nyquist condition has the following implications: ¯ ¾Ï . Then, the folded spectrum È½ ½ ´ Ò
There are gaps between copies of ´ µ. No matter how ½
Suppose that the symbol rate is so high that Ì
Ò
Ì µ looks like the one in Figure 4.3. ´ µ looks, the Nyquist condition cannot be satisﬁed and ISI is inevitable. ¯ ½
Suppose that the symbol rate is slower so that Ì
È
their neighbors. The folded spectrum ½ ½ ´
Ò ´µ ¾Ï . Then, copies of ´ µ can just touch
Ò Ì µ is ﬂat if and only if Ì for Ï ¼ for otherwise (4.10) The corresponding time domain function is the sinc pulse Ü´Øµ sinc´
4.5 Ø...
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This note was uploaded on 12/13/2012 for the course EEL 6535 taught by Professor Shea during the Spring '08 term at University of Florida.
 Spring '08
 Shea
 Frequency

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