| Novel nonlinear methods for high resolution spectral analysis of time domain signals, namely, the Filter Diagonalization Method (FDM) and Regularized Resolvent Transform (RRT), have been developed and applied to the signal processing problems in Nuclear Magnetic Resonance (NMR) experiments. Several important breakthroughs that significantly improve the efficiency and stability of FDM and RRT are discussed. They include the multi-scale Fourier-type basis, regularization of multi-dimensional FDM, and a doubling scheme for Constant-Time NMR signals. Applied to several 2D and 3D protein NMR experiments, substantial resolution enhancement has been demonstrated. Several qualitative and semi-quantitative ways of studying the reliability and sensitivity of FDM and RRT are discussed. Various issues that are specific to NMR spectral analysis are also addressed. |
