Mathematics Of Spectral Treatment In The Fourier Domain

James A. de Haseth

doi:10.1117/12.970714

20 December 1985 Mathematics Of Spectral Treatment In The Fourier Domain

James A. de Haseth

Proceedings Volume 0553, Fourier and Computerized Infrared Spectroscopy; (1985) https://doi.org/10.1117/12.970714
Event: 1985 International Conference on Fourier and Computerized Infrared Spectroscopy, 1985, Ottawa, Canada

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.

Citation Download Citation

James A. de Haseth "Mathematics Of Spectral Treatment In The Fourier Domain", Proc. SPIE 0553, Fourier and Computerized Infrared Spectroscopy, (20 December 1985); https://doi.org/10.1117/12.970714

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available