12, -0.543347179, -0.980775131, -0.398801013, 0.823661318, 0.286615541, -0.917042669, 0.995046175} work equally. The accuracy of discrete representation is however limited by how many digits are used. For example, sending {0.913410317, 0.662541770, 0.137126512, -0.543347179, -0.980775131, -0.398801013, 0.823661318, 0.286615541, -0.917042669, 0.995046175} is more accurate than sending the same information rounded to only three digits {0.913, 0.663, 0.137, -0.543, -0.981, -0.399, 0.824, 0.287, -0.917, 0.995} to represent the analogue signal of Figure 5.6(a). Broadband Telecommunications Technologies and Management 1 S Time Figure 5.7 Quantisation into binary levels The error thus introduced into discrete digital representation is known as quantisation noise. The required degree of accuracy is generally determined by the application which uses the received information, and/or by the applicable standard. In practice, digital transmission is carried out using binary numbers (that is using only O's and 1's) rather than decimal. The signal levels are converted to binary numbers using a set number of quantisation levels. This is demonstrated in Figure 5.7. Here, the maximum- minimum range of the input signal (-1 to 1) is divided into 16 levels, each level represented by binary numbers in the range of 0000 to 1111. Each discrete sample is then converted to a binary number based on the amplitude of the signal. The analogue signal can then be transmitted using binary bits as {1111, 1101, 1001, 0011, 0000, 0100, 1110, 1010, 0000, 1111}. The receiver can reproduce the analogue signal with the knowledge of the sampling rate, quantisation levels and the minimum-maximum range. The accuracy of digital representation clearly depends on the number of quantisation levels. The example in Figure 5.7 uses 16 levels, which yields a certain degree of accuracy while some information is lost. Here the first and the last samples are both represented by 1111, whereas their amplitude is clearly different. This can be remedied through increasi