Chemical rank estimation for second-order calibration by discrete Fourier transform coupled with robust statistical analysis

• A novel chemometric strategy has been developed to estimate accurately the chemical rank in overlapped signals.
• This method has been employed to resolve overlapped fluorescence to accurately quantify the analytes of interest.
• The performance of this method was comparable with the well-known CONCORDIA.

The accurate estimation of the underlying number of components in complex samples is critical in data analysis. A new chemometric strategy was developed in this study to determine accurately the number of underlying components in complex samples. First, discrete Fourier transformation was used to project the eigenvectors from the singular value decomposition to the frequency space. A robust statistical analysis based on iterative t-test was then employed to eliminate the outliers in the Fourier coefficients of each eigenvector. Finally, ANOVA was used to differentiate the meaningful components from noise. Simulated and published fluorescence datasets were used to demonstrate the strategy. Results indicate that the proposed strategy accurately and efficiently estimated the number of underlying components in the analyzed dataset. Moreover, the performance of the proposed method was comparable with the well-known core consistency diagnostic and Monte Carlo simulation coupled with frequency location methods. The new technique coupled with second-order calibration was successfully used to resolve the problem of seriously overlapped fluorescence spectra in the accurate quantification of fluoroquinolone antibiotics in tap water samples. Second-order advantage was achieved.