Application of the Filter Diagonalization Method to One- and Two-Dimensional NMR Spectra

A new non-Fourier data processing algorithm, the filter diago-nalization method (FDM), is presented and applied to phase-sensitive 1D and 2D NMR spectra. FDM extracts parameters (peak positions, linewidths, amplitudes, and phases) directly from the time-domain data by fitting the data to a sum of damped complex sinusoids. Grounded in a quantum-mechanical formal-ism, FDM shares some of the features of linear prediction and other linear algebraic approaches, but is numerically more effi-cient, scaling like the fast Fourier transform algorithm with re-spect to data size, and has the ability to correctly handle spectra with thousands or even millions of lines where the competing methods break down. Results obtained on complex spectra are promising. © 1998 Academic Press Key Words: filter diagonalization method (FDM); linear predic-tion; 2D NMR data processing; J spectroscopy; phase-twist lineshape