One method to get around this is to use an x/sin x
compensation or equalizer block to remove the NRZ signal. Now, when we cascade the equalizer with
the RC filter and the response of the NRZ signal, we satisfy Nyquist??™s ISI-free theorem.
h(t)
cos aapt
T b
1
4a2t2
T2
#
sin apt
T b
pt
T
MODULATION THEORY 55
BW ??“BW Ts Ts
Ts Ts
Ts Ts
+1 +1
??“1
x(t) Y2(t)
Y2(t)
Y1(t)
H( f )
pf Ts
sin(pfTs)
BW ??“BW
+1 +1
x(t) H( f )
sin(??f Ts)
pfTs
Compensation
Block
BW ??“BW
x(t) H( f )
?‡“
?‡“
??—
??“1
FIGURE 2.7 Decomposition of the NRZ pulse stream to illustrate the Nyquist zero-ISI case.
Square Root Raised Cosine (SRC) Filter. As discussed above, the receiver will also use some sort
of filtering and we would really like the zero-ISI criteria to hold in the receiver. Here we discuss the
possibility of using the transmit pulse-shaping filter in the receiver. If we used the RC filter in the transmitter,
then when another receiver filter is used, ISI will be present in the signal entering the detection
device and possibly significantly degrade performance. Another method is to evenly split up the RC
filter into two parts: the transmitter will use the SRC filter and the receiver will also use the SRC filter.
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