  Iterative filtering methods were introduced around 2010 to improve
definitions and measurements of structural features in signal processing. Like
many applied techniques, they present considerable challenges for
mathematicians to theorize their effectiveness and limitations in commercial
and scientific usages. In this paper we recast iterative filtering methods in a
mathematical abstraction more conducive to their understanding and
applications. We also introduce a new visualization of simultaneous local
frequencies and amplitudes. By combining a theoretical and practical
exposition, we hope to stimulate efforts to understand better these methods.
Our approach acknowledges the influence of Ciprian Foias, who was passionate
about pure, applied, and applications of mathematics.
