For example if the raised cosine spectrum is chosen

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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, ܴص from the raised cosine spectrum is not timelimited. Therefore, truncation and delay is required for realization. Finally, recall that ܴص is the overall response of the transmitted pulse passing through the ban- dlimited channel and the receiving filter. Mathematically, ´µ δ µ ¾ À ´ µÍ ´ µ ¾ where Í ´ µ, (4.14) Î ´ µ, and À ´ µ are the Fourier transform of ٴص, 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 ٴص is called the square-root raised-cosine pulse. Of course, suitable tru...
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