New Approach to Generalized Two-Dimensional Correlation Spectroscopy. III: Eigenvalue Manipulation Transformation (EMT) for Spectral Selectivity Enhancement

Abstract

This paper demonstrates the potential of eigenvalue manipulating transformation (EMT) of a data matrix for spectral selectivity enhancement, especially useful in 2D correlation analysis. The EMT operation aims at the accentuation of select features of the information content of the original data matrix. For example, by uniformly lowering the power of a set of eigenvalues associated with the original data, the smaller eigenvalues become more prominent and the contributions of secondary loadings become amplified. As a direct consequence of the minor factor accentuation by such EMT operations, 2D correlation spectra gain much stronger discriminating power. The selectivity enhancement effect of such manipulation of eigenvalues is much more noticeable on the synchronous 2D correlation spectrum. This improvement for the spectral selectivity of synchronous 2D correlation spectra is potentially very important, as we usually put more emphasis on the interpretation of asynchronous 2D spectra in 2D correlation analysis due to overlaps of synchronous peaks. Such EMT operations tend to exaggerate the information content of minor PCs and reduce that of major PCs. Thus, much more subtle difference of spectral behavior for each component is now highlighted. Surprisingly, asynchronous 2D correlation spectra are found to be much less sensitive to such EMT operations. The result indicates that the distinction of different band responses has already been accomplished effectively by the original asynchronous 2D correlation analysis.