Multiscale wavelet decomposition of Time-Resolved X-Ray diffraction signals in cyclohexadiene

Abstract

We demonstrate how the wavelet transform, which is a powerful tool for compression, filtering, and scaling analysis of signals, may be used to separate large- A nd short-scale electron density features in X-ray diffraction patterns. Wavelets can isolate the electron density associated with delocalized bonds from the much stronger background of highly localized core electrons. The wavelet-processed signals clearly reveal the bond formation and breaking in the early steps of the photoinduced pericyclic ring opening reaction of 1,3-cyclohexadiene, which are not resolved in the bare signal.