Cramer-Rao bound expressions for parametric estimation of overlapping peaks: Influence of prior knowledge

We have derived analytical expressions of the Cramer-Rao lower bounds on sp ectral parameters for singlet, doublet, and triplet peaks in noise, We cons idered 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 spect ral and experimental parameters, which is useful for quantitation objective s and experimental design. The influence of constraints (chemical prior kno wledge) on parameters of the peaks of doublets and triplets is demonstrated both analytically and numerically and the inherent benefits for quantitati on are shown. Our expressions also enable analysis of spectra comprising ma ny peaks. (C) 2000 Academic Press.