Data-driven time-frequency tessellation for signals with oscillatory amplitude envelopes and instantaneous frequency, with application to photoplethysmograhy

Abstract: Biomedical signals often comprise multiple non-sinusoidal oscillatory components whose amplitude modulation (AM) and instantaneous frequency (IF) may themselves be governed by additional (second-order) oscillatory dynamics with time-varying amplitude and frequency. We introduce a novel time-frequency (TF) analysis framework, {\em Tessellation-based Ensembled Time-Frequency Representation via Integrated Shifting} (TETRIS), designed based on the proposed generalized adaptive non-harmonic model to leverage second-order oscillatory information in this class of signals. We present the model and algorithm using the photoplethysmogram (PPG) as a canonical example, whose cardiac component is known to encode respiratory information in both AM and IF, and demonstrate how respiratory signals can be recovered from PPG. The central idea of TETRIS is to partition the TF plane along the estimated IF of the cardiac component and to process each partition adaptively to enhance representation quality. This tessellation enables a refined time-frequency representation (TFR), allowing more effective recovery of the respiratory modulation governing the AM of the cardiac component. We provide theoretical justification for the proposed method and validate its performance on semi-synthetic signals. Finally, we demonstrate that TETRIS enables improved reconstruction of multiple surrogate respiratory signals directly from PPG data. While the model and algorithm are developed with a focus on PPG, the framework is flexible and has potential to be applied to other signals.