ine component in the time series at a particular frequency. The sine (imaginary) computation only measures the sine component in the time series. The amplitude and phase of the signal can change but the frequency and wave shape remain the same. 27 A full treatment of modulation and error coding can be found in Data Over Radio, Varrall and Belcher, ISBN 0-930633-14-8, first published by Quantum Publishing 1992. Making Telecoms Work The periodic nature of sinusoids provides the basis for implementing orthogonal signals (signals that do not interfere with each other) in either the time or frequency domain. Being sinusoidal, the subcarriers can be arranged such that the peak signal energy of one subcarrier coincides with the minimum energy in the adjacent subcarrier (a property well known to designers of FFSK modems in the 1980s). This property provides the basis for OFDM signal orthogonality. If you want to find out whether a time series contains a sine or cosine component, create a cosine function at frequency F and a sine function at frequency F, multiply by the cosine function (which we will call real F (I) and multiply by the sine function, which we will call imaginary F (Q). Both should be nonzero values but any modulation applied will show up as sine and cosine offsets, or in other words, the IQ-modulated waveform. 2.13.6 The IDFT and DFT in Wide-Area OFDM (LTE) Wide-area OFDM, of which LTE is one example, implies a specific need to have a relatively slow symbol rate with an extended guard band (to deal with the delay spread on the channel) combined with the ability to support high data rates. Keeping the symbol rate down requires the implementation of a more complex FFT and/or higher-order modulation, for example the option of a 256-point FFT and/or 64 QAM. Note that these radio systems in common with WiFi are two way SO require both an inverse discrete Fourier transform to achieve the waveform synthesis on the transmit path and the discrete Fourier transform to achieve signal analysis on the receive path. As