The discrete Fourier transform is widely used in the applied sciences for the numerical approximation of the Fourier transform on the real line from sampled values of f. Despite the overwhelming success of this approximation, there are surprisingly few rigorous investigations and still substantial theoretical gaps when it comes to error estimates. Here we derive exact error estimates in terms of the decay and smoothness of f. Our analysis also provides the new insight of how the optimal spacing of the samples should depend on the decay and smoothness of f.
This is joint work with Karlheinz Gröchenig and Andreas Klotz.
https://univienna.zoom.us/j/67922750549?pwd=Ulh5L1QxNFhBOC9PUjlVdG9hc0tmUT09