  The nonlinear Fourier transform (NFT) has recently gained significant
attention in fiber optic communications and other engineering fields. Although
several numerical algorithms for computing the NFT have been published, the
design of highly accurate low-complexity algorithms remains a challenge. In
this paper, we present new fast forward NFT algorithms that achieve accuracies
that are orders of magnitudes better than current methods, at comparable run
times and even for moderate sampling intervals. The new algorithms are compared
to existing solutions in multiple, extensive numerical examples.
