Wavelet analysis of extended X-ray absorption fine structure data: Theory, application

Fourier transform (FT) plays an indispensable role in the quantitative analysis of extended X-ray absorption fine structure (EXAFS). The fitting of FT-EXAFS has already solved many scientific issues. However, FT is not well suited for signals which involve transient processes. More and more complex and obscure systems require to be studied with the development of modern science and technology, especially the complex system showing overlapped single-/multi-scattering pathways in EXAFS spectrum, the unknown system involving atoms with similar atom numbers and some other unusual systems that cannot be solved only by the conventional FT and fitting method. Wavelet transform (WT) of EXAFS spectrums discerns the contribution of each pathway not only in R-space but also in k-space at the same time. The maximums of k-R contour map of the WT coefficients' modulus represent the contributions of specific pathways. Together with a priori knowledge or analysis of the system, WT k-R map helps us better understand the local structure and improve the fitting model. The most critical issues of WT analysis are how to improve the resolution with the least loss of information, and how to identify the contributions of different pathways quickly and accurately. To meet wider applications in the future, the WT method for EXAFS analysis still need to be improved.