Correlation data processing for determining the averaged differential chromatogram in the case of multiple sample injections

The relationship between the input and output signals of a chromatograph is demonstrated. The expediency of improving the signal-to-noise ratio and using correlation data processing for this purpose is noted. An algorithm for calculating a chromatogram averaged over multiple injections of a sample from a specific individual specimen is presented. This algorithm is then modified for the case of calculating a differential averaged chromatogram, which is required to determine the difference in the component composition of two different specimens. A Legendre pseudorandom sequence is used to generate the input signals. The alphabet of this sequence is 1 or 0: 1 indicates a sample injection, and 0 indicates the absence of a sample injection at a given time. In the case of analyzing two specimens, the input sequences controlling the injection of the first and second specimens are complementary: if the sample of the first specimen is not injected, the sample of the second specimen is injected, and vice versa. The algorithm for calculating the averaged chromatogram is reduced to regression analysis. An information matrix of the experimental design is introduced. The accuracy of estimation is characterized using the covariance matrix of estimates. The choice of the optimal input sequence for sample injection is based on the D-optimality condition (the condition for maximizing the determinant of the information matrix), which ensures the minimum generalized variance of all estimates of the ordinates of the averaged chromatogram. The results of a numerical simulation experiment are presented, proving the effectiveness of using the correlation data processing method for averaging chromatograms.