While generalized two-dimensional correlation spectroscopy has several advantages, its theoretical framework limits the application area, i.e., one cannot carry out the correlation analysis for the intensity variations of such bands that are accompanied by shifts. In this respect, we have introduced new correlation indices which are invariant to band shifts. The conventional correlation indices are defined by the fixed spectral positions. Instead, the new correlation indices have been assigned to the individual spectral 'regions' for target bands. The theoretical framework has been described in this Letter together with the simulation for practical use.
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