Nonlinear spectral characterization of discrete data.

The explicit analytical expression of the nonlinear Fourier transform (NFT) of a finite set of data is provided. Then a simple recursion relation for the NFT is constructed as a function of the spectral parameter. These tools provide a complete characterization of the nonlinear coherent structures (solitons, breathers,...) present in numerical or experimental data representing the solution, at a given value of time, of a nonlinear evolution equation (e.g., of the nonlinear Schr\"odinger family). \textcopyright{} 1996 The American Physical Society.