ropriate time-domain section (a 3.2-microsecond burst in WiFi). A DFT analysis equation on the receive path multiplies the time-domain signal by a sinusoid and sums over the appropriate time domain section (3.2-microsecond burst). If it was a continuous signal (which it isn't) the transform would integrate rather than sum. 2.13.4 The IDFT and DFT as Used in a WiFi Transceiver Take a WiFi transceiver as an example. In essence, a WiFi transceiver is based on a mix of seventeenth century (Cartesian) and nineteenth-century (Fourier) mathematical principles. The modulation can either be BPSK, QPSK, 16 QAM or 64 QAM. Using a 16-QAM signal as an example, 4 data bits are mapped onto a 16-QAM constellation (based on Cartesian coordinates). The position of the symbol that relates specifically to the 4 bits is described as a complex number with two values, one of which describes the amplitude and the second of which describes the phase. The phase coordinate has a numerator j after it which can be +j or -j. The j numerator denotes whether the symbol is mapped to a positive or negative phase shift. These two values are then put into a bin and the process is repeated 52 times and then another 12 times using zeros as a value to make up 64 complex number bins. So, for example, in the 802.1 implementation of WiFi at 5 GHz the operational bandwidth can be anything between 100 and 455 MHz depending on the country. This compares with the 83 MHz allocated at 2.4 GHz for 802.11 b and g. This means that 802.11 a has anything up to 19 nonoverlapping channels of 20 MHz compared with the three nonoverlapping channels at 2.4 GHz. Physical Layer Connectivity Table 2.13 802.11 a data rates, modulation options and coding schemes Data rate 6/9 Mbps 12/18 Mbps 24/36 Mbps 48/54 Mbps Modulation 16 QAM 64 QAM Coding 1/2 2/3, 3/4 The channel spacing of 20 MHz supports an occupied bandwidth (-3 dB bandwidth) of 16.6 MHz that is subdivided down into 64 subcarriers spaced 312.5 kHz apart. The 64 subcarriers include 48 carriers for data, 4 pilot carrie