 radio systems. 3.2.5 Some Naming Issues For brevity and in due deference to Hans Rademacher and Mr Walsh, we shall describe these codes as Hadamard codes used as a Hadamard transform. As with the Fourier transform, the Hadamard transform computation can be decimated to speed up the computation process in which case it is known as a fast Hadamard transform (FHT). In some ways, the FHT is easier to implement computationally as it does not require the 'twiddle factors' implicit in the FFT. This is because the discrete FFT is approximating and then describing a composite sinusoidal waveform (hence the twiddle factors). The FHT is describing square waves and therefore does not need additional approximation correction factors. The fast Hadamard transform (FHT) is used on the receive path. The inverse fast Hadamard transform (IFHT) is used on the transmit path. As we have said, the FHT has properties that are distinct and different from the FFT (the fast Fourier transform) but are also complementary. The combination of the two techniques, the FHT and FFT together, deliver a number of specific performance advantages. These benefits should include cost reduction, improved coverage, improved capacity and more consistent and flexible radio access connectivity. 3.2.6 How the FHT and FFT Deliver Cost Reduction In the 1970s there was a consensus that it was going to be easier (cheaper) to filter in the time domain rather than the frequency domain and by implication, to process and filter in the digital domain rather than the analogue domain. Interrelationship of the Physical Layer with Other Layers of the OSI Model This started the process whereby channel spacing in cellular systems has relaxed from the 25 or 30 kHz used in first-generation systems to the 200 kHz used in GSM to the 1.25 MHz or 5 MHz systems used in present 3G networks. The process is taken further, for example in WiFi systems (20 MHz) and 3G systems (1.25 or 5 MHz) or advanced 3G systems (10,15,20 or 100 MHz). The objective is to reduce the cost of RF (radio 