Wavelet analysis of extended x-ray absorption fine structure data

Fourier transform (FT) is a fundamental step for the data reduction and interpretation of extended x-ray absorption fine structure (EXAFS) spectra. The FT separates backscattering atoms by their radial distance from the absorbing atom (so-called shells). We suggest to routinely complement the FT by a wavelet transform (WT), which provides not only radial distance resolution, but resolves in $k$ space. This information eases the discrimination of atoms by their elemental nature, especially if these atoms are at the same distance. We present an in-depth analysis of the Morlet wavelet, which has specific advantages for EXAFS analysis, including the possibility to estimate Morlet parameter values optimized either for elemental or for spatial resolution. Using an experimental spectrum of $\mathrm{Zn}\text{\ensuremath{-}}\mathrm{Al}$ layered double hydroxide, we demonstrate the discrimination of $\mathrm{Al}$ and $\mathrm{Zn}$ at a similar crystallographic position, in spite of destructive interference substantially reducing signal information. Finally, the extension to multiple scattering paths leads to a deeper understanding of the resolution properties of the WT.