New Insight into the Mathematical Background of Generalized Two-Dimensional Correlation Spectroscopy and the Influence of Mean Normalization Pretreatment on Two-Dimensional Correlation Spectra
Abstract:Generalized two-dimensional (2D) correlation spectroscopy is considered from the point of view of linear algebra. It is shown that a synchronous spectrum is the same as the cross-product matrix of the experimental data. An asynchronous spectrum is also treated as the ordered scalar products of the dynamic vectors of the experimental matrix and its Hilbert transformation. This approach connects the theory of generalized 2D correlation spectroscopy with the well-known conceptions of classic correlation analysis. The importance of spectral normalization in the 2D correlation analysis and its influence on the 2D correlation spectra is also investigated. All calculations were done on a synthetic spectral model consisting of two components. The synchronous spectra obtained from the model matrix were compared with those obtained after spectral mean normalization. It was found that the results strongly depend on the pretreatment. We plotted the Hilbert transformation of the meancentered model and found that the normalization leads to the disappearance of the asynchronous spectra in the two-component system. Also, it has been concluded that the influence of normalization is important just for the systems with large intensity variations. All the results presented here are quite general and can be applied irrespective of the nature of the perturbation.
Document Type: Research Article
Affiliations: Department of Chemistry, School of Science, Kwansei-Gakuin University, Uegahara, Nishinomiya 662-8501, Japan.
Publication date: March 1, 2001
More about this publication?
- The Society publishes the internationally recognized, peer reviewed journal, Applied Spectroscopy, which is available both in print and online. Subscriptions are included with membership or can be purchased by institutional or corporate organizations. Abstracts may be viewed free of charge. Previously published as Bulletin (Society for Applied Spectroscopy)
- Editorial Board
- Information for Authors
- Submit a Paper
- Subscribe to this Title
- Membership Information
- Request copyrighted SAS materials
- Spectroscopic Nomenclature
- Focal Point (Open Access)
- ingentaconnect is not responsible for the content or availability of external websites