Information Theory of Signal Resolution — Precision of Measurements

Abstract

Even a sophisticated signal processing suffers more or less from strong peak overlap or low signal-to-noise ratio. This discussion emphasizes not only the practical use of the Kalman filter but also the statistical and probabilistic aspects of it. The precision or relative standard deviation (RSD) of the estimates obtained from the Kalman filter is considered in a simple model where white noise is the only randomness. The RSD of the filter estimates is shown to be predicted from the degree of peak overlap and from the peak width and area with accuracy. The reliability of quantitative data can be evaluated with the predicted precision as a standard without repeated simulations. Mutual information has the equivalent meaning to the precision and is a useful concept for the optimization of instrumental conditions, especially for multi-peak output. The Kalman filter is selected as signal processing here on account of its mathematical simplicity and relevance to all the subjects discussed here.