APPLICATION OF DISCRETE FOURIER TECHNIQUES FOR THE IMPROVEMENT OF INFRARED SPECTROSCOPY DATA.

摘要

Because of the calculational speed of the fast Fourier transform (FFT) calculational algorithm for computing the discrete Fourier transform (DFT) and the usually small number of discrete components necessary to represent the data and its restoration, discrete Fourier techniques have been found to be the most efficient for data enhancement and restoration operations.; The thrust of this research has been the development of fast and efficient procedures for determining the continued Fourier spectrum, or the continued interferogram for FTS data, with the application of as many of the pertinent physical constraints as possible. The inverse DFT is a Fourier series, and the coefficients of the sinusoids are the discrete spectral components. This Fourier series is added to the function formed from the low frequency band, (or to the interferogram for FTS data) and the sum of the squared error is minimized in the total function to produce a set of linear equations in these high frequency coefficients for the constraint of finite extent, and a set of nonlinear equations for the constraint of minimum negativity. A variation of the method of successive substitutions was adapted that is very efficient in solving the set of nonlinear equations. The procedure to implement the constraint of minimum negativity has been found to easily accommodate the constraints of finite extent and the minimization of values above an upper bound also, so that all these constraints may be simultaneously applied to a given set of data. Further, the procedure to implement the constraint of minimum negativity has proven very insensitive to noise error.; The above procedures for implementing the constraints of finite extent and minimum negativity have proven successful in the restoration of both simulated and experimental infrared spectroscopy data. For infrared grating spectroscopy data the data are first inverse filtered, then the constraints are applied to continue the Fourier spectrum. For FTS data, it is the interferogram that is continued. In certain cases the interferogram is pre-multiplied by a suitable window function before extension in order to reduce the artifacts.