Time-Frequency Analysis: From Wireless Communications to Abstract Harmonic Analysis

In the talk I will discuss the relation between problems in wireless communications and time-frequency analysis. I will explain the basic principle of OFDM (orthogonal frequency division multiplexing) and its formulation in time-frequency analysis. Surprisingly, the so-called pulse-shaping problem is equivalent to a problem on twisted convolution, and its general solution requires experience in and tools from abstract harmonic analysis. Similarly, the modeling of the transmission channel leads to new and interesting problems on pseudodifferential operators. Their treatment is outside the standard theory of PDE and requires a genuine time-frequency approach. The talk is intended for a general audience and does not require any prerequisites.