rms and their associated iterative algorithms. Note that once upon a time many years ago I was advised by a publisher (not John Wiley) that every equation used in a book halved the number of books sold. Due to the fact that my understanding of higher level maths is at best tenuous I have enthusiastically embraced this advice ever since. So what follow is an explanation of the Fourier transform that eschews maths and/or diagrams (that I find difficult to draw and not helpful). Making Telecoms Work 2.13.3 Characteristics of the Fourier Transform Fourier's fundamental assertion that has made him famous through time is simply that any complex signal viewed in the frequency domain can be understood as a composite of a number of simple sinusoidal signals that have been added together. To place this into our specific context of interest (OFDM), his theorem led to the under- standing that a composite waveform can be described as a mix of sine and cosine waves (90 degrees apart) that also have specific phase and amplitude characteristics. More specifi- cally, signal points in the frequency domain can be combined to create complex signals in the time domain (the inverse Fourier transform) and complex time-domain signals can be resolved back into specific signal points in the frequency domain (the Fourier transform). If the process is applied to a discrete waveform sample (as in an OFDM signal burst of a defined and repetitive length), then it is described as a discrete Fourier transform (DFT) or inverse discrete Fourier transform (IDFT). The overall purpose of the Fourier transform in the context of implementing an OFDM transmitter and receiver is to take a complex time-varying waveform and express it as a tractable mathematical formula. Tractable implies an ability to either compact the formula itself and/or the data used in the formula - the basis for the algorithms used in fast Fourier transforms. An IDFT synthesis equation on the transmit path multiplies the discrete frequency domain by a sinusoid and sums over the app