rom Figure 10.23, the sinc function periodically passes a zero value at frequencies equal to integer multiples of f. It follows that if carriers are separated by exactly such integer multiples of f, then they will be orthogonal to each other if sampled at exactly these frequencies. This is illustrated in Figure 10.24, where three waveforms are transmitted together. It can be seen that at frequencies which are integer multiples of f, the interference from neighbouring carriers is zero. It means that carriers can be received orthogonally, that is without cross-carrier interference. In practice the available bandwidth to transmit a signal is divided into narrow bandwidth subcarriers. The subcarrier bandwidth is generally specified by standards: for example 4G LTE standards specify a subcarrier bandwidth of 15 kHz. Different standards have differ- ent subcarrier bandwidth as determined by their specific applications and available total bandwidth. An advantage of OFDM systems is the relatively inexpensive (in terms of processing requirement and device cost) discrete Fourier transform (DFT) technology it uses. DFT and inverse DFT (IDFT) techniques convert signals from the time domain to the frequency domain Broadband Telecommunications Technologies and Management equivalent and back. In most OFDM systems, the number of subcarriers is generally a power of 2 as DFT and IDFT sample sizes work best using these numbers. For example 4G LTE standards specify systems with 128, 256, 512 and 1024 subcarriers of narrow 15 kHz band- width [14]. An OFDM transmitter adjusts the transmission phase and amplitude of each individual subcarrier based on the signal constellation (e.g. 16-QAM symbols have different phase and amplitude). It can further adjust the amplitude and phase in response to variations of transmis- sion channel as described with respect to DSL systems in Chapter 9. For example the three subcarriers shown in Figure 10.24 may be individually controlled in response to varying signal constellation or channel conditions. T