t ways as will be discussed below. Analogue modulation was discussed in Chapter 3 in relation to voice telecommunications. Voice telecommunications as well as audio and video broadcasting were until recently carried out using analogue technologies such as amplitude or frequency modulation, and the band- width utilised for the modulated signal was equal to (in the case of amplitude modulation, AM) or greater than (in the case of frequency modulation, FM) the original baseband signal. In contrast, digital modulation techniques take at their input discrete symbols. These symbols may be 1's and O's, or a set of real numbers each representing one or more bits of data. For example the symbol set may be {-2, -1, 1, 2} where each symbol represents two bits of data: {00, 01, 10, 11}. Such configuration allows more data bits to be transmitted over a unit of bandwidth, and therefore higher transmission rates given a fixed frequency resource. As will be seen below, transmission rates can be increased by a factor of two or more using different digital modulation techniques if channel conditions are favourable. This allows for transmit- ting at channel capacity rates as predicted by the Shannon theorem: more bits/s data rates per unit of bandwidth may be carried by the channel as the received signal quality improves (see Figure 4.7). In contrast, analogue modulation techniques cannot utilise the bandwidth in a similar manner: a 4 kHz bandwidth voice signal needs a minimum 4 kHz channel. A carrier frequency can be represented as a cosine waveform, A cos (2 ft + A), specified by its amplitude (A), frequency (f) and starting phase (0). The modulation process is about varying the amplitude, frequency or phase of the carrier signal according to the input data (e.g. 0 or 1). These techniques are, respectively, known as ASK, FSK and PSK. Broadband telecommuni- cations systems commonly use ASK and PSK, or a combination of the two: that is, transmission data may be embedded within the amplitude A, phase 0, or both. FSK is not used and 