Codes and Expansions (CodEx) Seminar

Karlheinz Gröchenig (University of Vienna)
How well does the discrete Fourier transform approximate the Fourier transform on R?

In order to compute the Fourier transform of a function \(f\) on the real line numerically, one samples \(f\) on a grid and then takes the discrete Fourier transform. We derive exact error estimates for this procedure in terms of the decay and smoothness of \(f\). The analysis provides an asymptotically optimal recipe of how to relate the number of samples, the sampling interval, and the grid size.

This is joint work with Martin Ehler and Andreas Klotz.