Causality-preserving synchrosqueezed time–frequency analysis: methodology, diagnostics, and trade-offs

Synchrosqueezed time–frequency analysis is widely used to improve energy concentration and instantaneous frequency estimation in nonstationary signals. Despite its effectiveness, standard synchrosqueezing relies on non-causal kernels and reassignment rules that may introduce time–frequency energy prior to the physical onset of a signal, potentially compromising temporal interpretability in applications where causality is essential. In this work, I propose a causality-preserving formulation of synchrosqueezed time–frequency analysis in which temporal admissibility is enforced directly within the reassignment and thresholding framework. Causality is treated as a structural property of the time–frequency representation rather than as a post-processing constraint. To quantify the effects of causality enforcement, I introduce diagnostic metrics that explicitly measure causality violations, ridge stability, and energy localization. Using analytically defined synthetic signals with known ground truth, I perform a systematic comparison between standard and causality-preserving synchrosqueezed representations. The results demonstrate that enforcing causality eliminates non-physical pre-onset energy by construction and yields improved ridge stability and reduced off-ridge energy leakage, while maintaining comparable instantaneous frequency accuracy across a broad range of noise levels. A sensitivity analysis further shows that the resulting trade-offs can be controlled through thresholding and smoothing parameters without requiring fine tuning. The proposed framework provides a transparent and physically interpretable extension of synchrosqueezed time–frequency analysis, particularly suited for applications where temporal causality and onset consistency are critical.