This repository accompanies the article “A deterministic information-adaptive time coordinate for multiscale state space analysis of non-stationary signals.” It presents a fully deterministic framework for re-parameterizing time, in which the time axis is adjusted according to the local informational structure of a signal. Instead of changing signal amplitudes or using stochastic or learning-based models, the method constructs a strictly monotonic, information-adaptive time coordinate derived from a technical measure of local information density. Information-rich signal segments are stretched in time, while information-poor intervals are compressed, preserving the original temporal sequence of events and the topology of the signal. Coherent state space representations and parallel multiscale state fields (micro, meso, and macro scales) are constructed on this adaptive time coordinate. All scales share the same adaptive temporal parameter and differ only in their integration or smoothing behavior. This enables a direct, point-by-point comparison of scale-dependent dynamics without resampling or interpolation. On this basis, phenomena such as multiscale decoupling and time-delayed recoherence can be quantified purely geometrically and reproducibly. All processing steps are completely deterministic and explicitly parameterized. Translated with DeepL.com (free version)
Kevin Junginger (Thu,) studied this question.