Quantification of chromatographic data using a matched filter: robustness towards noise model errors

Abstract The robustness towards noise model errors of a matched filter used for the quantification of chromatographic data is investigated mathematically and by using computer simulations. It is shown that the matched filter is robust under the assumption of first order band-limited noise. Two extremes of this model suffice for most situations. For these extremes, i.e., for a very small or a very large value of the noise time constant, the filter reduces to a cross-correlation with the signal model and to the second derivative of the signal model multiplied by −1, respectively. When the matched filter is made part of a procedure in which signal model errors are corrected by optimization of the filter performance, the noise model is critical at low signal-to-noise ratios and the correct model is to be preferred.