Talk on September 18, 2024 at The CUNY Graduate Center

Subtitle: Towards a compositional theory of nonlinear signal processing.

Abstract:The Volterra series is a model of nonlinear behavior that extends the convolutional representation of linear and time-invariant systems to the nonlinear regime. Though well-known and applied in electrical, mechanical, biomedical, and audio engineering, its abstract and especially compositional properties have been less studied. In this talk, we present an approach to categorifying the Volterra series, in which a Volterra series is defined as a functor on a category of signals and linear maps, a morphism between Volterra series is a lens map and natural transformation, and together, Volterra series and their morphisms assemble into a category, which we call Volt. We study three monoidal structures on Volt, and outline connections of our work to the field of time-frequency analysis. We also include an audio demo.

Paper link: https://arxiv.org/abs/2308.07229