The matrix pencil as a tunable filter.

Despite inherent sensitivity constraints, nuclear magnetic resonance (NMR) plays an indispensable role in probing molecular structures and dynamics across scientific disciplines. Remarkably, while extensive efforts have targeted instrumental and experimental sensitivity improvements, comparatively little focus has been dedicated to sensitivity enhancement through signal analysis. Amidst this present gap, the matrix pencil method (MPM) has emerged as a versatile algorithm that offers tunable filtering and phasing capabilities. Extensive prior research has established the MPM as an adept fitting tool in signal analysis. Here, the efficacy of the MPM is investigated by precisely modeling noisy data to separate information-bearing signals from noise, thereby expanding its utility in various magnetic resonance applications. Simulated data is used to confirm the ability of the MPM to discern and separate signals from noise. Comparative analyses against standard Fourier-based filtering methods highlight the superior performance of the matrix pencil filter (MPF) in preserving signal fidelity without introducing aliasing artifacts. A variety of experimental data is then explored to demonstrate the proficiency of the MPF in characterizing signal components and correcting phase distortions. Collectively, these case studies underscore the filtering capacity of the MPM, portending its use for analytical sensitivity improvements in a wide range of NMR applications.

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.