Schwarz representation for matching and similarity analysis

This paper presents a novel multiscale representation of one-dimensional signal based on complex analysis. We show that a signal and its derivative at different scales can be represented by one analytic function defined on the unit disc in the complex plane, which is called the Schwarz representation of a signal. This representation is applied to the matching problem. Using the theory of analytic functions, we are able to define the inverse of a signal. The matching function between two signals can be defined as the composition of one signal´s Schwarz representation and another signal´s inverse. The matching function determined by this method has a group structure and is close-formed