Here we pass these impulses through an ideal brick wall filter,
in order to provide the transmit pulses (see Fig. 2.3).
The Nyquist filter and theorem have essentially two issues associated with them. The first issue
is the impractical implementation of the ideal brick wall (Nyquist) filter. It is well known that band-limited
52 CHAPTER TWO
FIGURE 2.1 Overview block diagram emphasizing the filtering operations.
FIGURE 2.2 Example of a received signal??™s eye diagram.
BW ??“BW Ts Ts
+1 +1
??“1
+1 +1
??“1
x(t) y1(t) H(f)
FIGURE 2.3 Nyquist??™s ISI-free transmission.
Modulator HR( f ) Demodulator HT( f )
Overall Filter (Tx and Rx) Eye Diagram
??“1.5
??“1
??“0.5
0
0.5
1
1.5
0 12 16
Normalized Symbol Time (Ts/8)
Eye Value
8 4
signals cannot be time limited [4]. The second issue is the impulse train carrying the information to
the input of the Nyquist filter. The first issue can be solved if we use practical filters that have a frequency
response that is symmetrical around the 3-dB transition point. A commonly used filter that
exhibits the symmetrical property is the raised cosine (RC) filter. The symmetry, in response, is used
for providing linear phase and thus constant time delays for all in-band frequency components [5??“8].
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