A signal-processing tool adapted to the periodic biphasic phenomena: the Dynalet transform.

The article focuses on the Dynalet transform, a generalization of the Fourier transform based on the van der Pol equation, for approximating periodic biphasic biological signals such as cardiac and respiratory rhythms. Unlike classical linear transforms relying on orthogonal bases derived from simple or damped pendulum models, the Dynalet transform uses asymptotically stable limit cycles from anharmonic pendulum dynamics, providing better fits for asymmetric physiological signals with fewer parameters. Applications demonstrated include mechanical and electrical cardiac activity, ventricular volume, pulse, and lung volume signals, where the Dynalet transform often outperforms or matches Fourier transform accuracy while offering greater physiological interpretability. The study also situates the Dynalet approach within a broader framework called the Adapted Approximation Approach (AAA), which emphasizes physiologically plausible, potentially non-orthogonal bases tailored to the underlying biological mechanisms, and discusses its relevance for modeling complex phenomena such as epidemic waves.