"Nonuniform fast Fourier transforms and the fast sinc transform"Kircheis, MelanieThe well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial as well as in the frequency domain. This generalization is referred to as nonuniform fast Fourier transform (NNFFT). In this talk an interesting signal processing application of the NNFFT, the fast sinc transform, is presented. We suggest an approximate algorithm for the fast computation of the discrete sinc transform, which can be viewed as truncated version of the famous Sampling Theorem of Shannon-Whittaker-Kotelnikov. Here we utilize the approximation of the sinc function by an exponential sum, which results in a fast sinc transform consisting of two steps – a precomputation of weights and the application of two NNFFTs. By an appropriate choice of weights we are able to state an error estimate for the fast sinc transform. |
| http://univie.ac.at/projektservice-mathematik/e/talks/Kircheis_2021-06_abstract.pdf |
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