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Unformatted text preview: ctrum 4.7 3 Wong & Lok: Theory of Digital Communications 4. ISI & Equalization HC ( f ) AWGN
Figure 4.7: Dispersive channel model
less sensitive to timing errors than the sinc pulse. Just like all other bandlimited pulses, Ü´Øµ from the
raised cosine spectrum is not timelimited. Therefore, truncation and delay is required for realization.
Finally, recall that Ü´Øµ is the overall response of the transmitted pulse passing through the ban- dlimited channel and the receiving ﬁlter. Mathematically, ´µ Î´ µ ¾
À ´ µÍ ´ µ ¾ where Í ´ µ, (4.14) Î ´ µ, and À ´ µ are the Fourier transform of Ù´Øµ, Ú ´Øµ, and ´Øµ, respectively. Given that an ISI-free spectrum ´ µ is chosen, we can employ (4.14) to obtain the simple case of a ban- dlimited channel, i.e., the channel does not introduce any distortion within its passband, we can simply
choose Í ´
Õ also Õ µ to be ´ µ. Then the Fourier transform the transfer function of the matched ﬁlter is
´ µ. For example, if the raised-cosine spectrum is chosen, the resulting ISI-free pulse Ù´Øµ is called the square-root raised-cosine pulse. Of course, suitable tru...
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- Spring '08