Introduction to wavelet applications in surface spectroscopies

In experimental sciences, recorded data are often modelled as the noisy convolution product of an instrumental response with the ‘true’ signal. High‐resolution electron energy‐loss spectroscopy (HREELS) and x‐ray photoelectron spectroscopy (XPS) constitute two examples of this. A series of three papers is proposed about an estimation method of this ‘true’ signal in the particular cases of HREELS and XPS. This method uses wavelets that, as functions well localized in time and frequency, are properly adapted to signal analysis. In this first article, the wavelet theory is introduced and its rapid expansion is justified by a comparison of the wavelet transform with the Fourier transform. Afterwards, in order to illustrate the efficiency of the wavelet approach, some wavelet‐based signal analysis tools are presented. These tools include: filtering of a noisy signal, localization of irregular signal structures such as singularities or peaks and deconvolution itself. Copyright © 2004 John Wiley & Sons, Ltd.