k in 2004 with RL Hudson applied the concepts of fractal geometry and fractal transforms to the evaluation of risk in financial markets - the science of fiscal transforms. A profit and loss statement, balance sheets and share price movements are mathematical expressions and are therefore amenable to fiscal mathematical trend and pattern analysis. Fractal transforms are particularly good at exposing patterns and coupling effects in fiscal systems. Back in the engineering rather than fiscal domain, fractal transforms are increasingly relevant to the modelling of offered traffic behaviour in multimedia networks. We revisit this topic in Chapter 12. Like Cooley and Tukey, Mandelbrot's work continues to inspire mathematicians to pro- duce faster and more effective transforms both for signal-processing and image-compression applications. Note in passing how pure maths (maths for its own sake) and applied maths requires certain infrastructural conditions in order to flourish and deliver political, social and economic value. Plato's academy and the Alexandrian Library (387 BC to AD 529), the growth of Islam after 650 AD, the Gutenberg Press in 1450, the postal service that allowed Newton to correspond with his peers and more recently the internet are examples of changes that have facilitated mathematical progress. 2.13.2 How Fourier Transforms Deliver Performance Differentiation Present radio systems including DAB/DVB-T and DRM, WiFi and LTE HSOPA all depend on the Fourier transform in order to support relatively high data rates. As bit rates have increased over the radio physical layer it has become progressively more attractive to use orthogonal frequency division multiplexing (OFDM) to improve re- silience to intersymbol interference. An early example in terms of a European specification is the DAB standard (1991) but OFDM is now a fundamental part of local area WiFi sys- tems and used in LTE mobile broadband networks. Let us briefly review the differentiation achievable through optimised implementation of the transfo