Bayesian Spectrum Analysis on Quadrature Nmr Data with Noise Correlations

Abstract

In NMR data analysis a great deal of prior information is available. We know, in general terms, what characteristic signal will be received, that for quadrature measurements it will be the same in both channels and that the noise is potentially correlated. We have shown in previous work [1], [2] that when prior information is incorporated into the analysis of data, the frequencies, decay rates, and amplitudes may be estimated much more precisely than by using the discrete Fourier transform directly. Here we extend the Bayesian analysis to include the quadrature nature of the data and noise correlations. We then show that in typical NMR data the frequencies and decay rates may be estimated with a precision several orders of magnitude better than directly from the discrete Fourier transform.