Methods to extract exclusively linear relationships in generalized two-dimensional correlation spectroscopy (2DCOS)

Abstract

The theory and terminology for two-dimensional correlation spectroscopy (2DCOS) was originally developed for time-dependent periodic perturbation functions. Later, the 2DCOS theory was further extended also to include non-periodical perturbations. Then, because of the difficulty with the concept of synchronicity, it was recently proposed to exchange this concept to the concept of linearity. It was shown that the synchronous (covariance) maps expressed peaks that represented both linear and nonlinear relationships between pairs of spectral bands, while the asynchronous (disvariance) maps expressed peaks that exclusively represented nonlinear relationships. The present paper proposes two novel methods to eliminate or reduce expression of peaks in the synchronous (covariance) maps that represent nonlinear relationships. The idea behind these proposed methods is the simple fact that nonlinear relationships cannot give very high correlation coefficients. By using one of these simple proposed methods and well resolved spectral bands the 2DCOS analysis will give two matrices and maps, the modified covariance (synchronous) map giving peaks that exclusively represent linear relationships and the disvariance (asynchronous) map giving peaks that exclusively represent nonlinear relationships. The two methods are validated and illustrated using two examples, one simulated data set and one real Fourier transform infrared (FTIR) spectroscopy evaporation data set.