 Analogue to Digital 1 S Time 1s Time Figure 5.6 Analogue waveform to digital using a 10 Hz sampling rate needed to find how analogue and discrete signals were related to each other in terms of the necessary transmission band [3]. Nyquist showed that for a digital representation of a band-limited signal, sampling must be done at a rate of more than twice the largest frequency component. Given the Nyquist rate, and exact measurement of the signal at the sampling point, the analogue signal can be perfectly represented in a digital form. The band-limited condition is important as signals may have high frequency components. For example, human voice has frequency components are mostly in the range of 300-3400 Hz, as shown in Figure 5.4. However, some higher frequency components do exist, especially for people who have higher voices. However, since telecommunication channels are band limited, the normal practice is to filter the analogue signal to within that limited band by removing all higher frequency components. For voice this means limiting voice to 4000 Hz. While higher filtering can lead to higher fidelity reproduction, it comes at the expense of extra bit rate. Nyquist theorem therefore mandates that a voice signal must be sampled at a rate of larger than 2x4000=8000 Hz. If we assume that the highest frequency component of the analogue signal in Figure 5.5(a) is 5 Hz, then the sampling rate can be as low as 10 Hz, which will result in a discrete representation as shown in Figure 5.6. Note that this representation is equally accurate as those of Figure 5.5(c) and (d). That is, sampling at any higher rate does not yield any advantage for the analogue to digital conversion process. As discussed before, telecommunications is the science and technology of conveying information to a remote location. From this point of view continuous analogue waveform or discrete numbers are equivalent. That is, the sending of the analogue waveform in Figure 5.6(a) and the following set of numbers {0.913410317, 0.662541770, 0.1371265