48 Point-to-Point Protocols and Links Chap.2 h(t) 222222222 Figure 2.8 Impulse response h(t)for which H(f)=0 for f =0.Note that the area over which h(t)is positive is equal to that over which it is negative. around 0,as illustrated in Fig.2.8;this phenomenon is often called ringing.This type of impulse response suggests that the NRZ code is not very promising for a bandpass channel. To avoid the foregoing problems,most modems for bandpass channels either di- rectly encode digital data into signals with no dc component or else use modulation techniques.The best known direct encoding of this type is Manchester coding (see Fig.2.9).As seen from the figure,the signals used to represent 0 and 1 each have no dc component and also have a transition (either I to-1 or-I to 1)in the middle of each signaling interval.These transitions simplify the problem of timing recovery at the receiver (note that with the NRZ code,timing recovery could be difficult for a long run of 0's or 1's even in the absence of filtering and noise).The price of eliminating dc components in this way is the use of a much broader band of frequencies than required. Manchester coding is widely used in practice,particularly in the Ethernet system and the corresponding IEEE 802.3 standard described in Section 4.5.There are many other direct encodings,all of a somewhat ad hoc nature,with varying frequency characteristics and no de component. 2.2.5 Modulation One of the simplest modulation techniques is amplitude modulation (AM).Here a signal waveform s(t)(called a baseband signal)is generated from the digital data as before, say by the NRZ code.This is then multiplied by a sinusoidal carrier,say cos(2 fot),to generate a modulated signal s(t)cos(2 fot).It is shown in Problem 2.6 that the frequency representation of this modulated signal is [S(f-fo)+S(f+fo)1/2 (see Fig.2.10).At the receiver,the modulated signal is again multiplied by cos(2 fot),yielding a received signal r(t)=s(t)cos(2πfot) s()s()cos(4r fot) (2.12) 2 2 n Figure 2.9 Manchester coding.A binary I is mapped into a positive pulse followed by a negative pulse.and a binary 0 is mapped into a negative pulse followed by a positive pulse.Note the transition in the middle of each signal interval.48 Point-to-Point Protocols and Links Chap. 2 r Figure 2.8 Impulse response h(t) for which H(f) = 0 for f = O. Note that the area over which h(t) is positive is equal to that over which it is negative. around 0, as illustrated in Fig. 2.8; this phenomenon is often called ringing. This type of impulse response suggests that the NRZ code is not very promising for a bandpass channel. To avoid the foregoing problems, most modems for bandpass channels either di￾rectly encode digital data into signals with no dc component or else use modulation techniques. The best known direct encoding of this type is Manchester coding (see Fig. 2.9). As seen from the figure, the signals used to represent 0 and I each have no dc component and also have a transition (either I to -lor -I to I) in the middle of each signaling interval. These transitions simplify the problem of timing recovery at the receiver (note that with the NRZ code, timing recovery could be difficult for a long run of O's or l's even in the absence of filtering and noise). The price of eliminating dc components in this way is the use of a much broader band of frequencies than required. Manchester coding is widely used in practice, particularly in the Ethernet system and the corresponding IEEE 802.3 standard described in Section 4.5. There are many other direct encodings, all of a somewhat ad hoc nature, with varying frequency characteristics and no dc component. 2.2.5 Modulation One of the simplest modulation techniques is amplitude modulation (AM). Here a signal waveform s(t) (called a baseband signal) is generated from the digital data as before, say by the NRZ code. This is then multiplied by a sinusoidal carrier, say cos(27rJot), to generate a modulated signal s(t) cos(27rfat). It is shown in Problem 2.6 that the frequency representation of this modulated signal is [S(f - fa) + S(f + fo)]/2 (see Fig. 2.10). At the receiver, the modulated signal is again multiplied by cos(27rfat), yielding a received signal r(t) = s(t) cos2 (27rfat) s(t) s(t) cos(47rfat) =2+ 2 (2.12) o o o t-. Figure 2.9 Manchester coding. A binary I is mapped into a positive pulse followed by a negative pulse. and a binary 0 is mapped into a negative pulse followed by a positive pulse. Note the transition in the middle of each signal interval