 a signal at each stage of reception as it progresses through a telecommunications system. For example, a voice call may go through several exchanges between the caller and the called parties as illustrated in Figure 5.8. The electronic devices at each stage add noise to the signal, and the cumulative result can be quite large. A long-distance telephone call quality worsens the more exchanges it passes through. The impact of noise can be demonstrated by considering the analogue waveform of Figure 5.9. The amount of noise added at each stage (from top to bottom) is noise with a power equal to one-tenth of the signal. It can be seen that as noise accumulates, the analogue signal is more and more distorted. The added noise is a random signal. While filtering and other processing may reduce the noise power, they cannot completely remove it. As a result, noise accumulates at each stage, and degrades signal quality. Analogue long-distance phone calls were famous for being noisy. The contrast in voice quality between long-distance and local calls was SO great that people used to say that a call was SO clear 'as if one was talking just across the town'. Digital communications however enables noise-free signal reproduction. Consider the binary digital and noise signals in Figure 5.10. While the noise cannot be calculated and removed, the received signal can be detected as whether a 1 or a -1 (denoting a 0) was trans- mitted. When that decision has been made, the signal can be reproduced without any noise. In this way noise accumulation is stopped. Digital telecommunications are not immune to noise however. If the level of additive noise is high, signal detection may become erroneous. Figure 5.11 and Figure 5.12 demonstrate this problem. When the power of signal compared with the power noise (SNR) is low, some bits may be erroneously detected. This gives rise to an important parameter in digital telecommu- nications, which is how many errors are received as noise level increases. This parameter is known as the bit error ra