Topology-Preserving Deformations of Digital Audio
Topology provides global invariants for data as well as spaces of deformation. In this paper we discuss the deformations of audio signals which preserve topological information specified by sublevel set persistent homology. It is well known that the topological information only changes at extrema. We introduce box snakes as a data structure that captures permissible editing and deformation of signals and preserves the extremal properties of the signal while allowing for monotone deformations between them. The resulting algorithm works on any ordered discrete data hence can be applied to time and frequency domain finite length audio signals.