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Published as SEP Report, 105, 167-176 (2000)

Multi-dimensional Fourier transforms in the helical coordinate system

James Rickett and Antoine Guitton,


For every two-dimensional system with helical boundary conditions, there is an isomorphic one-dimensional system. Therefore, the one-dimensional FFT of a 2-D function wrapped on a helix is equivalent to a 2-D FFT. We show that the Fourier dual of helical boundary conditions is helical boundary conditions but with axes transposed, and we explicitly link the wavenumber vector, ${\bf k}$, in a multi-dimensional system with the wavenumber of a helical 1-D FFT, $k_h$. We illustrated the concepts with an example of multi-dimensional multiple prediction.