A statistical analysis of NMR spectrometer noise

Abstract

Estimation of NMR spectral parameters, using e.g. maximum likelihood methods, is commonly based on the assumption of white complex Gaussian noise in the signal obtained by quadrature detection. Here we present a statistical analysis with the purpose of discussing and testing the validity of this fundamental assumption. Theoretical expressions are derived for the correlation structure of the noise under various conditions, showing that in general the noise in the sampled signal is not strictly white, even if the thermal noise in the receiver steps prior to digitisation can be characterised as white Gaussian noise. It is shown that the noise correlation properties depend on the ratio between the sampling frequency and the filter cut-off frequency, as well as the filter characteristics. The theoretical analysis identifies conditions that are expected to yield non-white noise in the sampled signal. Extensive statistical characterisation of experimental noise confirms the theoretical predictions. The statistical methods outlined here are also useful for residual analysis in connection with validation of the model and the parameter estimates.