Telecommunications (modulation, OFDM)

Level AdvancedDifficulty ★★★★★Application⌖ Open in the map

What is it?

Sending bits over the air by modulating sinusoidal carriers in amplitude and phase (complex numbers). OFDM splits the band into many orthogonal subcarriers using an inverse FFT at the transmitter and an FFT at the receiver — Wi-Fi, 4G/5G and DSL.

Formulas

$s(t) = \operatorname{Re}\big\{(I + iQ)\,e^{2\pi i f_c t}\big\}$
QAM: one complex number per symbol

The mathematics behind it

Fourier transform★★★★★fundamental
OFDM (Wi-Fi, 4G/5G, DSL) sends data on many orthogonal subcarriers using inverse FFT and FFT.

This page has the essentials. A fuller treatment (intuition, formal definition, worked example) is on the way.