A family of smoothing algorithms for electron and other spectroscopies based on the Chebyshev filter

Smoothing is a useful tool to improve the signal-to-noise ratio of spectroscopic data. This paper reports a new family of smoothing formulas, the Chebyshev filters, which are derived approaching the original data to a polynomial and using the mini-max principle, that is, keeping the maximum error down to a minimum, as fitting criterion. The properties of the filters are studied analyzing their associated transfer functions in the frequency domain. This leads us to the concept of spectral window and spectral window width as tool and parameter, respectively, to remove the high frequency noise components accompanying the experimental data. Also, simple criteria to choose the appropriate width of the spectral windows are put forward. The behaviour of the filters is easy to understand and the filters are fast and simple to use and to program. Finally the proposed smoothing algorithms have been tested using synthetic data as well as X-ray photoelectron spectra and optical absorption spectra.