Cramér-Rao Bound Expressions for Parametric Estimation of Overlapping Peaks: Influence of Prior Knowledge

We have derived analytical expressions of the Cramér-Rao lower bounds on spectral parameters for singlet, doublet, and triplet peaks in noise. We considered exponential damping (Lorentzian lineshape) and white Gaussian noise. The expressions, valid if a sufficiently large number of samples is used, were derived in the time domain for algebraic convenience. They enable one to judge the precision of any unbiased estimator as a function of the spectral and experimental parameters, which is useful for quantitation objectives and experimental design. The influence of constraints (chemical prior knowledge) on parameters of the peaks of doublets and triplets is demonstrated both analytically and numerically and the inherent benefits for quantitation are shown. Our expressions also enable analysis of spectra comprising many peaks.