Multi-dimensional Fourier transforms in the helical coordinate system

James Rickett and Antoine Guitton

james@sep.stanford.edu, antoine@sep.stanford.edu

ABSTRACT

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.