DIGITAL-FILTERS FOR IMPROVED RESOLUTION ENHANCEMENT IN SPECTRAL-ANALYSIS

Abstract

A new set of digital filters for the analysis of complex spectral data is introduced. These filters are based on the consecutive application of two zero-area square-wave or Gaussian filters and are, in fact, convolutions of the individual filters. It is shown that these filters are also even and of the zero-area type. Analytical expressions for both zero-area square-wave and Gaussian filters combined are presented. It is found that the signals, obtained with the individual and combined filters as well, are characterized by a strong positive central peak, situated at the centroid of the spectral line, and two negative side lobes. A remarkable difference is the presence of two positive sidebands when the combined filters are used. Criteria to exclude detection of these sidebands, using both individual and combined filters, have been developed. For numerical work, it has been found that it is more efficient to use two consecutive zero-area filters rather than the corresponding convolved filters. In the first part of the present work, the technique has been tested on simulated spectral data, where statistical noise has been introduced by using a Gaussian pseudorandom generator. The technique proposed here (consecutive application of two individual zero-area filters or use of the convolution expressions) has a number of advantages over a single filtering operation: (1) the constant, linear, quadratic, and cubic terms in a polynomial background contribution to the signal are eliminated (this property has been generally proved); (2) the resolution enhancement as well as the signal-to-noise ratio can be improved by using two identical filters and the following working interval for the filter widths M, 0.25 fwhm(s) less-than-or-equal-to M less-than-or-equal-to fwhm. (fwhm. is the full width at half-maximum of the signal); (3) the broadening of the convolution signal with the combined filters for Voigt profiles is less pronounced with increasing damping constants a; and (4) the use of combined filters or the application of two consecutive zero-area filters is a clear improvement over a single filtering operation, and even over Zimmermann's method, for the unraveling of multiplets composed of strongly overlapping lines. In the second part of this paper, successful applications to the following spectroscopic techniques are described: inductively coupled argon plasma optical emission spectrometry, solid-state NMR, IR, and UV-vis absorption spectrometry.