reas a digital signal is represented by a limited number of discrete values with sudden changes between varying signal levels. An analogue signal can be represented as s(t) = M(t)sin(2ft+0) (2.1) where M(t) is the amplitude (varying in time), f is the frequency, and O is the phase of the signal. Any signal can be represented using these fundamental parameters. In contrast to the analogue signal, which contains only one harmonic, a digital signal is represented by a square wave, which is composed of odd-integer harmonics. A square wave can be repre- sented by the following infinite Fourier series: (2.2) An ideal square wave requires that the signal changes from the high to the low state instantaneously. This requires infinite harmonics to be added and would need infinite bandwidth for transmission. In fact, transmitting a signal at a high modulation rate through a band-limited channel can create Intersymbol Interference. Therefore, a pulse is shaped before its transmission. The purpose of pulse shaping is to make the transmitted signal better suited to the communication channel by limiting the effective bandwidth of the transmis- sion. By filtering the transmitted pulses this way, the intersymbol interference caused by the channel can be kept in control. When the digital signal is passed through a real channel (of limited bandwidth), effects like ringing or ripple are exhibited. Figure 2.2 illustrates these effects on the square wave when the Fourier series is truncated to only 7, 11, and 21 terms, respectively. Chapter 2 Data Transmission human 2.2 Square wave composed of increasing numbers of odd-integer harmonics: (a) 7 harmonics, (b) 11 harmonics, (c) 21 harmonics. Transmitter Receiver System System Serial Transmission of Information (1 byte) Using Only One Channel Transmitter Receiver System System Sequence of 8 Bits (1 byte) Sent in Parallel from Transmitter to Receiver Using a Bus of 8 Channels Fig. 2.3 (a) Serial and (b) parallel transmission. Serial and Parallel Transmission Data can be sent in either ser