Data processing in NMR relaxometry using the matrix pencil

The matrix pencil method (MPM) is explored for stable, reproducible data processing in nuclear magnetic resonance (NMR) relaxometry. Data from one-dimensional and two-dimensional relaxometry experiments designed to measure transverse relaxation T₂, longitudinal relaxation T₁, diffusion coefficient D values, and their correlations in a standard olive oil/water mixture serve as a platform available to any NMR spectroscopist to compare the performance of the MPM to the benchmark inverse Laplace transform (ILT). The data from two practical examples, including the drying of a solvent polymer system and the enzymatic digestion of polysialic acid, were also explored with the MPM and ILT. In the cases considered here, the MPM appears to outperform the ILT in terms of resolution and stability in the determination of fundamental constants for complex materials and mixtures.