Intensity Enhancement of a Two-Dimensional Asynchronous Spectrum Without Noise Level Fluctuation Escalation Using a One-Dimensional Spectra Sequence Change

Abstract

Previously, we demonstrated that the intensities of cross-peaks in a two-dimensional asynchronous spectrum could be enhanced using sequence change of the corresponding one-dimensional spectra. This unusual approach becomes useful when the determination of the sequential order of physicochemical events is not essential. However, it was not known whether the level of noise in the two-dimensional asynchronous spectrum was also escalated as the sequence of one-dimensional spectra changed. We first investigated the noise behavior in a two-dimensional asynchronous spectrum upon changing the sequence of the corresponding one-dimensional spectra on a model system. In the model system, bilinear data from a chromatographic–spectroscopic experiment on a mixture containing two components were analyzed using a two-dimensional asynchronous spectrum. The computer simulation results confirm that the cross-peak intensities in the resultant a two-dimensional asynchronous spectrum were indeed enhanced by more than 100 times as the sequence of one-dimensional spectra changed, whereas the fluctuation level of noise, reflected by the standard deviation of the value of a two-dimensional asynchronous spectrum at a given point, was almost invariant. Further analysis on the model system demonstrated that the special mathematical property of the Hilbert–Noda matrix (the modules of all column vectors of the Hilbert–Noda matrix being a near constant) accounts for the moderate variation of the noise level during the changes of the sequence of one-dimensional spectra. Next, a realistic example from a thermogravimetry–Fourier transform infrared spectroscopy experiment with added artificial noise in seven one-dimensional spectra was studied. As we altered the sequence of the seven FT-IR spectra, the variation of the cross-peak intensities covered four orders of magnitude in the two-dimensional asynchronous spectra. In contrast, the fluctuation of noise in the two-dimensional asynchronous spectra was within two times. The above results clearly demonstrate that a change in the sequence of one-dimensional spectra is an effective way to improve the signal-to-noise level of the two-dimensional asynchronous spectra.