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Proceedings Paper

Mathematics Of Spectral Treatment In The Fourier Domain
Author(s): James A. de Haseth
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Paper Abstract

The basic premise of Fourier domain processing is that the Fourier transform does not alter the information content of a spectrum. Spectra have traditionally been recorded in the frequency, wavelength or wavenumber domain, and this is referred to as the spectral domain. The Fourier transform of a spectrum converts the data to the time, wavenumber or retardation domain, known as the Fourier domain. Data manipilation is often carried out in the Fourier domain, particularly Fourier self-deconvolution, smoothing, and differentiation. These operations involve convolution in the spectral domain, which is equivalent to a multiplication in the Fourier domain. It is mathematically less expensive to achieve these operations in the Fourier domain. Other data handling operations can be achieved in the Fourier domain. The first of these is the Gram-Schmidt orthogonalization of raw GC/FT-IR spectrometry interferograms to construct infrared-based chromatograms. Search systems and structure elucidation methods can also be effectively carried out using Fourier transforms of absorption spectra.

Paper Details

Date Published: 20 December 1985
PDF: 7 pages
Proc. SPIE 0553, Fourier and Computerized Infrared Spectroscopy, (20 December 1985); doi: 10.1117/12.970714
Show Author Affiliations
James A. de Haseth, University of Georgia (United States)

Published in SPIE Proceedings Vol. 0553:
Fourier and Computerized Infrared Spectroscopy
David G. Cameron; Jeannette G. Grasselli, Editor(s)

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