Quadrature Orthogonal Signal Corrected Two-Dimensional Correlation Spectroscopy

Abstract

Orthogonal signal correction (OSC) removes a substantial part of the spectral response that is orthogonal to the selected external variable. The combined use of OSC filtering and two-dimensional (2D) correlation analysis was proposed in the previous study (Wu, Noda, Meersman, and Ozaki, J. Mol. Struct., 2006, paper in press) to enable one to obtain high-quality 2D correlation spectra by eliminating any information unrelated to the external variables. However, the direct application of OSC to two-dimensional (2D) correlation analysis will result in the loss of the component that is significantly perpendicular to the external variable but also is the portion significant to the asynchronous 2D correlation analysis. Therefore, in order to avoid the problem of losing the valuable asynchronous 2D correlation information, the present study proposes a modified OSC filtering method, which is called quadrature OSC (QOSC) filtering. By replacing the external variable vector y used for OSC filtering with a two-column Y matrix consisting of y and its Hilbert–Noda transformation, the component of the spectral data asynchronously correlated to the external variable y is preserved. The performance of this technique on two simulated spectra data sets with a strong contaminant band and systematic noises has demonstrated that QOSC filtering 2D correlation analysis enables not only the elimination of the influence of signals that are unrelated to the external variable but also the preservation of the portions of information in the data matrix that are 90 degrees out of phase with y. It enables OSC 2D to deal with the problems of losing the portion of information that is perpendicular to the external variable y but is quite significant to the 2D correlation analysis.