DIGITAL-FILTERS FOR IMPROVED RESOLUTION ENHANCEMENT IN SPECTRAL-ANALYSIS

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, co nvolutions of the individual filters. It is shown that these filters a re also even and of the zero-area type. Analytical expressions for bot h zero-area square-wave and Gaussian filters combined are presented. I t 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 sideban ds when the combined filters are used. Criteria to exclude detection o f these sidebands, using both individual and combined filters, have be en developed. For numerical work, it has been found that it is more ef ficient to use two consecutive zero-area filters rather than the corre sponding convolved filters. In the first part of the present work, the technique has been tested on simulated spectral data, where statistic al noise has been introduced by using a Gaussian pseudorandom generato r. The technique proposed here (consecutive application of two individ ual zero-area filters or use of the convolution expressions) has a num ber of advantages over a single filtering operation: (1) the constant, linear, quadratic, and cubic terms in a polynomial background contrib ution to the signal are eliminated (this property has been generally p roved); (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-e qual-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 i ncreasing damping constants a; and (4) the use of combined filters or the application of two consecutive zero-area filters is a clear improv ement over a single filtering operation, and even over Zimmermann's me thod, for the unraveling of multiplets composed of strongly overlappin g lines. In the second part of this paper, successful applications to the following spectroscopic techniques are described: inductively coup led argon plasma optical emission spectrometry, solid-state NMR, IR, a nd UV-vis absorption spectrometry.