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Unformatted text preview: developed in Section 4.2 can
be easily generalized to the above communication system. Letting
condition for no ISI is that the folded spectrum ½
Ò ½ ´µ ÀÌ ´ µÀ ´ µÀÊ ´ µ, the ´ µ, is constant for all frequencies, i.e.,
Ò Ì Ì (4.15) One method to achieve the Nyquist condition is to ﬁx the receiving ﬁlter to be the matched ﬁlter,
i.e., set ÀÊ ´ µ £
ÀÌ ´ µÀ £ ´ µ, and choose the transmission ﬁlter so that (4.15) is satisﬁed. This is the Nyquist pulse design method described in Section 4.2. The major disadvantage of this pulseshaping method is that it is in general difﬁcult to construct the appropriate analog ﬁlters for ÀÌ ´ µ and ÀÊ ´ µ in practice. Moreover, we have to know the channel response À ´ µ in advance to construct
the transmission and receiving ﬁlters.
An alternative method is to ﬁx the transmission ﬁlter4 and choose the receiving ﬁlter ÀÊ ´ µ to satisfy the condition in (4.15). As for the previous method, it is also difﬁcult...
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- Spring '08