Shannon Information Retrieved from Overlapped Chromatographic Peaks with Kalman Filter

Abstract

A function (FUMI) which describes the Shannon mutual information in chromatography is derived. FUMI covers two subjects in one formula: (i) the degree of peak overlap and the noise level; (ii) the mathematical formalism of peak deconvolution and quantitation based on the one-dimensional Kalman filter for peak resolution. Computer simulation demonstrates that a sufficient amount of mutual information can be retrieved from overlapped peaks (Gaussian) through (i) observation and (ii) data processing. A practical advantage of FUMI is logical evaluation and optimization of chromatographic experiments without resort to experience: the optimal can be defined as the chromatogram which can transmit the maximal amount of mutual information in a unit time.