Matching using Schwarz integrals

摘要

In this paper 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. This representation (called Schwarz representation) is applied to the matching problem. By 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 the other's inverse. The matching function determined by this method has a group structure and is in closed form.