Universal Factorizations of Quasiperiodic Functions

Abstract

Chirped sinosoids and interferometric phase plots are functions that are not periodic, but are the composition of a smooth function and a periodic function. These functions functions factor into a pair of maps: from their domain to a circle, and from a circle to their codomain. One can easily imagine replacing the circle with other phase spaces to obtain a general quasiperiodic function. This paper shows that under appropriate restrictions, each quasiperiodic function has a unique universal factorization. Quasiperiodic functions can therefore be classified based on their phase space and the phase function mapping into it.