Highly accurate smoothing filter

Abstract

An iterative filter for the smoothing of degraded line shapes with Gaussian noise, and a signal to noise ratio defined in a wide interval 20–∞ is presented. The smoothed line shape shows errors below 2% in its height and width parameters with regard to the true values used in the simulation. The filter reduces the Gaussian noise to less than a half. In the tests carried out with a PC computer, the new filter proved that the original line shape for a linewidth of 5–30 is better recovered than the Savitsky–Golay filter. The application of the procedure only involves the use of the linewidth parameter of the degraded peak which simplifies the smoothing process. The filter follows two basic operations: first, an oversmoothing is applied to the degraded line and second, an iterative enhancement on the oversmoothing spectrum is made. The resulting spectrum of these two operations is compared with the degraded line by a least squares fitting method. When the filter is used in a simplified version, it is useful not only to determine very overlapped lines in a degraded spectrum, but also to calculate the background in an experimental spectrum.