The general theory of Fourier self-deconvolution, i.e., spectral deconvolution using Fourier transforms and the intrinsic line-shape, is developed. The method provides a way of computationally resolving overlapped lines that can not be instrumentally resolved due to their intrinsic linewidth. Examples of the application of the technique to synthetic and experimental infrared spectra are presented, and potential applications are discussed. It is shown that lines in spectra having moderate signal/noise ratios (∼1000) can readily be reduced in width by a factor of 3. The method is applicable to a variety of spectroscopic techniques.

Fourier Self-Deconvolution: A Method for Resolving Intrinsically Overlapped Bands

There is an increasing awareness that the separation of over-lapping bands by the mathematical technique of curve fitting offers many pitfalls and should not be undertaken lightly. This review discusses critically the various factors involved, with particular reference to vibrational band systems; other types of overlapping band systems encountered in analytical work are considered in less detail. Five parameters are involved: the number of component bands, their positions, shapes and widths, and the form of the baseline. Curve fitting, by a least squares optimization method to a suitable goodness of fit criterion, is considerably facilitated if approximate values for some of the parameters are known at the outset. The methods available for peak finding are discussed and, although not free from problems, are reasonably effective. Similarly, band shapes can usually be defined semiquantitatively. However, it is seldom possible to obtain prior information on band widths; these should be determined during the curve fitting calculations. Although statistical goodness of fit criteria are available they should be used in conjunction with a visual plot, to locate any regions of poor fit. Furthermore, the overriding consideration must always be that the computer fit is plausible in terms of acceptable chemical species for the system being examined.

The Scope and Limitations of Curve Fitting

Application hints for Savitzky-Golay digital smoothing filters

A procedure is described for the measurement of clinically relevant concentrations of glucose in aqueous solutions with near-infrared (NIR) absorbance spectroscopy. A glucose band centered at 4400 cm-1 is used for this analysis. NIR spectra are collected over the frequency range 5000-4000 cm-1 with a Fourier transform spectrometer. A narrow-band-pass optical interference filter is placed in the optical path of the spectrometer to eliminate light outside this restricted range. This configuration provides a 2.9-fold reduction in spectral noise by utilizing the dynamic range of the detector solely for light transmitted through the filter. In addition, a novel spectral processing scheme is described for extracting glucose concentration information from the resulting absorbance spectra. The key component of this scheme is a digital Fourier filter that removes both high-frequency noise and low-frequency base-line variations from the spectra. Numerical optimization procedures are used to identify the best location and width of a Gaussian-shaped frequency response function for this Fourier filter. A dynamic area calculation, coupled with a simple linear base-line correction, provides an integrated area from the processed spectra that is linearly related to glucose concentrations over the range 1-20 mM. The linear calibration model accurately predicted glucose levels in a series of test solutions with an overall mean percent error of 2.5%. Based on the uncertainty in the parameters defining the calibration model and the variability of the magnitudes of the integrated areas, an overall uncertainty of 7.8% was estimated for predicted glucose concentrations.

Determination of physiological levels of glucose in an aqueous matrix with digitally filtered Fourier transform near-infrared spectra.

Comparison of inorganic interferences in atomic absorption spectrometric determination of arsenic and selenium

A number of signal processing operations can be carried out on spectra using a digital filter based on a simple trapezoid function. The filter is applied to the Fourier transform of the spectral signal. Several signal processing examples are presented to illustrate the capabilities of this filter. These examples include filtering and diagnosis of high frequency noise on a signal, removal of fixed frequency noise, minimization of quantization noise, and differentiation and approximate deconvolution for the purpose of resolution enhancement.

A Simple and Versatile Fourier Domain Digital Filter

Frequency response plots for Savitzky-Golay filter functions

A hardware cross-correlator has been developed as a readout system for a photodiode array spectrometer. With this system a reference spectrum is stored in a transient recorder and used as an electronic correlation mask for the detection and measurement of the same spectral signal. The correlator is described and then applied to the detection of Ca and Cr emission signals from an inductively coupled plasma source. The applicability of this correlator to the detection of a specific spectral pattern in the presence of a more complex partially overlapping spectral signal is also illustrated.

K. R. Betty

Papers

A Simple and Versatile Fourier Domain Digital Filter

Frequency response plots for Savitzky-Golay filter functions

Correlation readout system for a photodiode array spectrometer applied to inductively coupled plasma emission spectroscopy

Inexpensive lock-in amplifiers based on integrated circuit phase-locked loops

Autocorrelation analysis of noisy periodic signals utilizing a serial analog memory