PASF: Persistence-Aware Spectral Filtering for Test-Time Adaptation in Sleep Staging

Physiological signal models generalize poorly across devices, sensor configurations, and recording protocols. Such acquisition shifts frequently manifest in the frequency domain, motivating spectral adaptation at test time. However, a recording's marginal spectrum reflects not only acquisition conditions but also the task-relevant physiological states it contains and their prevalence. Wholesale alignment can therefore suppress state-dependent physiology alongside domain nuisance, particularly under label shift. We study source-free test-time adaptation and identify cross-state-persistent spectral shifts as a conservative correction target. These persistent shifts remain consistent across physiological states, while state-specific disagreement serves as counterevidence against full correction. We instantiate this principle as Persistence-Aware Spectral Filtering (PASF), which estimates probability-weighted state-conditioned spectral residuals relative to compact source templates. Their shared component shapes a recording-specific, phase-preserving filter, while the shared-energy fraction gates its strength. PASF processes each complete recording in two passes without target labels, raw source recordings, model updates, or gradients. Across four sleep-staging datasets comprising 740 recordings, PASF achieves four-domain mean balanced accuracies of 75.56% with U-Sleep and 74.30% with a CNN–Transformer. These results improve on source-only inference by 3.79 and 5.78 percentage points, respectively. Controlled comparisons show reduced composition-induced false correction and improved recovery under shared spectral distortion. Analyses of real recordings support cross-state persistence, while experiments beyond sleep staging identify the applicability and limits of the shared-shift principle.