A Methodological Framework for Analyzing and Differentiating Daily Physical Activity Across Groups Using Digital Biomarkers from the Frequency Domain

Human daily physical activity (PA), monitored via wearable devices, provides valuable information for real-time health assessment and disease prevention. However, analyzing time-domain PA data is challenging due to large data volumes and high inter- and intra-individual heterogeneity. Traditional PA analyses often rely on demographics, while advanced methods utilize time-domain summary statistics (e.g., L5, M10) or functional principal component analysis (FPCA). This study presents a data-efficient approach utilizing the Discrete Fourier Transform (DFT) to convert time-domain data into a compact set of frequency-domain variables. Our research suggests that adding these DFT variables can significantly enhance model performance. We demonstrate that incorporating DFT-derived variables substantially improves model performance. Specifically, (1) a small subset of DFT variables effectively captures major PA levels with effective dimensionality reduction; (2) these variables retain known associations with factors like age, sex, and weekday/weekend status; (3) they enhance the performance of classifiers. Mathematical and empirical analyses further confirm the reliability and interpretability of DFT-based features in dimension reduction. Across three mental health studies, these DFT-derived variables successfully capture key PA characteristics while retaining known associations and strengthening model performance. Overall, the proposed DFT-based framework offers a robust and scalable tool for analyzing accelerometer data, with broad applicability in health and behavioral research.