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Joseph Boccuzzi

"Signal Processing for Wireless Communications"

8
0.8
0.9
0.9
1
Normalized Frequency (Hz)
Magnitude, ???H( f )???
Ideal
?± = 0.1
?± = 0.5
?± = 1.0
FIGURE 2.4 Raised cosine frequency response.
54 CHAPTER TWO
Eye Diagram Using RC with ?± = 0.2
??“2
??“1.5
??“1
??“ 0.5
0
0.5
1
1.5
2
0 8 12 16
Normalized Symbol Time (Ts /8)
Eye Value
4
FIGURE 2.5 Raised cosine (  0.2) eye diagram.
We define zero ISI or ISI free as having overlapping pulses that do not interfere with one another
at the symbol sampling points: An eye diagram of a signal using
an RC filter is shown in Fig. 2.5. Here the zero-ISI requirements are clearly visible at the sampling
instances.
h(nTS)  0 4 n 
1,
2,c.
Eye Diagram Using RC with ?± = 0.9
??“1.5
??“1
??“0.5
0
0.5
1
1.5
0 12 16
Normalized Symbol Time (Ts /8)
Eye Value
8 4
FIGURE 2.6 Raised cosine (  0.9) eye diagram.
We show two eye diagrams corresponding to two roll-off factors,   0.2 and   0.9 (see
Figs. 2.5 and 2.6). These eye diagrams show that as we use more bandwidth beyond the Nyquist band,
there is less jitter in the transition regions of the symbols. Also the transitional overshoots are larger for
the smaller values of the roll-off factor due to the increase in the amplitude of the temporal tails of the
impulse response.


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