Explore the Novel Relationship of Time-Frequency Domains in Multivariate Signals: A Dynamic System Perspective

Objective: Time and frequency domains are two common dimensions used to characterize multivariate signals (MS). Previous research on the relationship between these two domains has mainly focused on how frequency components, such as power or phase, evolve over time. However, there may exist other unexplored relations between the time and frequency domains of MS. Methods: The study considers MS as a large-scale system and identifies its fundamental dynamic modes (DMs) with mutual orthogonality, regarding them as individual subsystems. Each DM encapsulates not only the spatial information but also displays a unique oscillatory frequency. The MS data at each time point is then projected onto these DMs, obtaining the DM-based time-frequency representation (DTFR). Results: Using electroencephalogram signals from three common brain diseases as illustrations, the results demonstrate that DTFR outperforms traditional time-frequency analysis approaches in disease discrimination. Conclusion: The DTFR reveals a novel relationship between the time and frequency domains of MS, namely how the subsystems of MS, each with its own characteristic oscillatory frequency, shape the dynamics of the overall large-scale system over time. Furthermore, the DTFR allows for the analysis of high-order interactions among all-lead signals as they change over time. Finally, the decomposition of DTFR can further uncover the time-frequency-topology relationships of MS from the perspective of dynamic systems. Significance: The DTFR approach expands the understanding of the relations between the time and frequency domains of MS, revealing new phenomena that have been unachievable by traditional methodologies, which might be widely used in many areas in the future.