Regularization of the two-dimensional filter diagonalization method: FDM2K

We outline an important advance in the problem of obtaining a two-dimension al (2D) line list of the most prominent features in a 2D high-resolution NM R spectrum in the presence of noise, when using the Filter Diagonalization Method (FDR I) to sidestep limitations of conventional FFT processing. Alth ough respectable absorption-mode spectra have been obtained previously by t he artifice of "averaging" several FDM calculations, no 2D line list could be directly obtained from the averaged spectrum, and each calculation produ ced numerical artifacts that were demonstrably inconsistent with the measur ed data, but which could not be removed a posteriori. By regularizing the i ntrinsically ill-defined generalized eigenvalue problem that FDM poses, in a particular quite plausible way, features that are weak or stem from numer ical problems are attenuated, allowing better characterization of the domin ant spectral features. We call the new algorithm FDM2K. 2000 Academic Press .