||Multi-dimensional Fourier transforms in the helical coordinate
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Published as SEP Report, 105, 167-176 (2000)
Multi-dimensional Fourier transforms in the helical coordinate
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,
, in a
multi-dimensional system with the wavenumber of a helical 1-D FFT,
We illustrated the concepts with an example of multi-dimensional