Progress on the two-dimensional filter diagonalization method. An efficient doubling scheme for two-dimensional constant-time NMR

An efficient way to treat two-dimensional (2D) constant-time (CT) NMR data using the filter diagonalization method (FDM) is presented. In this scheme a pair of N- and P-type data sets from a 2D CT NMR experiment are processed jointly by FDM as a single data set, twice as large, in which the signal effectively evolves in time for twice as long. This scheme is related to "mirror-image" linear prediction, but with the distinction that the data are directly used, without any preprocessing such as Fourier transformation along one dimension, or point-by-point reflection. As the signal has nearly perfect Lorentzian line shape in the CT dimension, it can be efficiently handled by the FDM approach. Applied to model and experimental signals, the scheme shows significant resolution improvement, and appears to tolerate noise reasonably well. Other complex aspects of multidimensional FDM are discussed and illustrated.