Two-Dimensional (2D) NMR Methods

2 Data Processing Methods: Fourier and Beyond

Vladislav Orekhov^1,*, Paweł Kasprzak^2,3, and Krzysztof Kazimierczuk³

¹ Department of Chemistry and Molecular Biology, Swedish NMR Centre, University of Gothenburg, 40530, Gothenburg, Box 465, Sweden² Faculty of Physics, University of Warsaw, 02-093, Warsaw, Pasteura 5, Poland³ Centre of New Technologies, University of Warsaw, 02-097, Warsaw, Banacha 2C, Poland^* Corresponding Author

2.1 Introduction

The modern NMR signal processing, which emerged with the introduction of Fourier NMR at the beginning of the 1970s is still a rapidly developing field due to demands posed by the introduction of evermore complex experiments and analyses as well as because of tremendous advances in mathematics, algorithms, and computer hardware. In this chapter, we attempt to present a compact overview of both practical and rigorously mathematical aspects of modern NMR signal processing.

2.2 Time-domain NMR Signal

As explained in previous chapter, in an NMR experiment, the radio-frequency (RF) pulse generates a coherent precession of the affected, polarized nuclear magnetic moments. The precession, in turn, induces an oscillating voltage in the receiver coil. The signal measured this way decays with time as the spin system returns to its thermal equilibrium and is called free induction decay (FID). The analytical shape of an NMR signal stems, to a good approximation, from the equation of motion of the magnetic moment exposed to the combination of constant ...