Maximum entropy signal processing in practical NMR spectroscopy

Abstract

NMR spectroscopy is intrinsically insensitive, a frequently serious limitation especially in biochemical applications where sample size is limited and compounds may be too insoluble or unstable for data to be accumulated over long periods. Fourier transform (FT) NMR was developed by Ernst¹ to speed up the accumulation of useful data, dramatically improving the quality of spectra obtained in a given observing time by recording the free induction decay (FID) data directly in time, at the cost of requiring numerical processing. Ernst also proposed that more information could be obtained from the spectrum if the FID was multiplied by a suitable apodizing function before being Fourier transformed. For example (see ref. 2), an increase in sensitivity can result from the use of a matched filter¹, whereas an increase in resolution can be achieved by the use of gaussian multiplication^1,3, application of sine bells^4–8 or convolution difference⁹. These methods are now used routinely in NMR data processing. The maximum entropy method (MEM)¹⁰ is theoretically capable of achieving simultaneous enhancement in both respects¹¹, and this has been borne out in practice in other fields where it has been applied. However, this technique requires relatively heavy computation. We describe here the first practical application of MEM to NMR, and we analyse ¹³C and ¹H NMR spectra of 2-vinyl pyridine. Compared with conventional spectra, MEM gives considerable suppression of noise, accompanied by significant resolution enhancement. Multiplets in the ¹H spectra are resolved better leading to improved visual clarity.