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 via a change of the sequence of the corresponding 1D spectra. This unusual approach becomes useful when the determination of the sequential order of physicochemical events is not essential. However, we have not known whether the level of noise in the 2D asynchronous spectrum is also escalated as the sequence of 1D spectra is changed. Herein, we firstly investigate the noise behavior in a two-dimensional asynchronous spectrum upon changing the sequence of the corresponding 1D spectra on a model system. In the model system, bilinear data from a chromatographic-spectroscopic experiment on a mixture containing two components are analyzed via 2D asynchronous spectrum. The computer simulation results confirm that the cross peaks intensities in the resultant 2D asynchronous spectrum are indeed enhanced by more than100 times as the sequence of 1D spectra is changed, whereasthe fluctuation level of noise, reflected by the standard deviation of the value of a 2D asynchronous spectrum at a given point, is almost invariant. Further analysis on the model systems demonstrates that the special mathematical property of the Hilbert-Noda matrix (the modules of all the column vectors of the Hilbert-Noda matrix is near a constant) accounts for the moderate variation of the noise level during the changes of the sequence of 1D spectra. Secondly, a realistic example from a thermogravimetry-Fourier transform infrared spectroscopy (TG-FTIR) experiment with added artificial noise in seven 1D spectra was studied. As we alter the sequence of the seven FTIR spectra, the variation of the intensities of cross peaks covers four orders of magnitudes in the 2D asynchronous spectra. In contrast, the fluctuation of noise in 2D asynchronous spectra is within two times. The above results clearly demonstrate that a change in the sequence of 1D spectra is an effective way to improve the signal-to-noise level of the 2D asynchronous spectra.

A new approach to recognizing the correct pattern of cross-peaks from a noisy 2D asynchronous spectrum by detecting intrinsic symmetry via the Kolmogorov–Smirnov test

“…(2) Enhancement of the intensities of cross-peaks: these approaches try to improve the signal-to-noise level of a 2D asynchronous spectrum by enhancing the intensities of crosspeaks. [42][43][44][45][46][47] Although these approaches are free from the problem of signal distortion, the signal-to-noise level of the treated 2D asynchronous spectrum using these approaches still cannot meet the practical requirement in many cases. (3) Extraction of useful spectral features from the noisy 2D correlation spectrum via statistical analysis: statistical analysis has been proved to be effective to enhance our understanding of the behavior of noise in 2D asynchronous spectra.…”