| Data processing techniques have become quite common throughout the Nuclear Magnetic Resonance (NMR) community as the development of high-dimensionality NMR experiments has progressed. High-dimensional NMR experiments are limited by the amount of time that they take to acquire. But data processing techniques can allow these experiments to be performed much more quickly, possibly providing much more information than was previously possible. Methods such as linear prediction and the filter diagonalization method have been developed to perform this task. Linear prediction is an effective method that is easy to use, but it can produce very poor results in some cases. The filter diagonalization method performs much more consistently than linear prediction, but can be complicated to use. The regularized resolvent transform and the extended Fourier transform are derived from the same basis as the filter diagonalization method. They can take advantage of the power of this method, but are much easier to implement. The derivation of these methods, along with their implementation is presented. One of the main difficulties associated with all data processing methods is the instability or “ill-conditioning” of the procedure, a discussion of the treatment of this problem in the framework of the regularized resolvent transform is also presented. Finally, some specific applications of these methods to problems that are difficult to address with the filter diagonalization method are introduced. The merits of these data processing schemes for NMR spectral analysis is evident from these examples. |
