A theoretical framework will be developed to analyze, estimate and track motion transformations in signals. The approach relies on Lie algebras that describe geometry and motion. The construction proceeds to Lie groups and their representations in the function spaces of signals.This method further derives continuous wavelets and all the related tools necessary for motion analysis. This theoretical framework will be presented with examples taken in the Galilei group of velocity, and in the group of rotational motion. Illustrations will demonstrate the efficiency of this approach for signal processing.