Smoothing of digital spectroscopic data by using a Chebyshev filter

Least-squares polynomial smoothing (LSP) is widely used for smoothing spectroscopic data. It is a very old technique described in many books on numerical analysis used to improve the signal-to-noise ratio of data. It was first applied by Savitzky and Golay in 1964. Later, in 1980, it was improved by Proctor and Sherwood by estimating values for the points which are normally lost by the central point smoothing as used by Savitzky and Golay. However smoothing by long LSP sequences leads to transmission zeros, phase reversal, and overshoots that are a drawback in some applications. In this work, an alternative method, the Chebyshev smoothing filter, is used to reduce the high-frequency noise in spectroscopic applications. Comparison in the frequency domain of the Chebyshev filter with other smoothing filters is also presented. Finally some application examples using XPS are given. (C) 2002 Elsevier Science Ltd. All rights reserved.