  It will be shown how to map a simple one-dimensional tight binding model with
a cosine potential in one dimension exactly to a two dimensional tight binding
model with periodic boundary conditions with the presence of a single flux
quantum spread evenly on the torus. The mapping is is achieved by a partial
sequence of "Fast Fourier Transform" (FFT) steps which if completed would be an
exact Fourier transform of the original model. Each step of the FFT recursively
maps a tight binding model into two decoupled sublattices of half the lattice
length.
