Abstract
Non-linear Fourier Transforms (NFTs) enable the analysis of signals governed by certain non-linear evolution equations in a way that is analogous to how the conventional Fourier transform is used to analyse linear wave equations. Recently, fast numerical algorithms have been derived for the numerical computation of certain NFTs. In this paper, we are primarily concerned with fast NFTs with respect to the Korteweg-de Vries equation (KdV), which describes e.g. the evolution of waves in shallow water. We find that in the KdV case, the fast NFT can be more sensitive to numerical errors caused by an exponential splitting. We present higher order splittings that reduce these errors and are compatible with the fast NFT. Furthermore we demonstrate for the NSE case that using these splittings can make the accuracy of the fast NFT match that of the conventional NFT.
Original language | English |
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Title of host publication | Proceedings 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) |
Place of Publication | Piscataway, NJ, USA |
Publisher | IEEE |
Pages | 4524-4528 |
ISBN (Electronic) | 978-1-5386-4658-8, 978-1-5386-4657-1 |
ISBN (Print) | 978-1-5386-4659-5 |
DOIs | |
Publication status | Published - 2018 |
Event | 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018: Signal Processing and Artificial Intelligence: Changing the World - Calgary Telus Convention Center (CTCC), Calgary, Canada Duration: 15 Apr 2018 → 20 Apr 2018 https://2018.ieeeicassp.org |
Conference
Conference | 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 |
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Country/Territory | Canada |
City | Calgary |
Period | 15/04/18 → 20/04/18 |
Internet address |
Bibliographical note
Accepted Author ManuscriptKeywords
- Fourier transforms
- Differential equations
- Signal processing algorithms
- Boundary conditions
- Scattering
- Computational complexity
- Europe
- Non-linear Fourier transform
- exponential splittings
- Korteweg-de Vries equation