Topological Time Frequency Analysis of Functional Brain Signals.

We present a novel topological framework for analyzing functional brain signals using time-frequency analysis. By integrating persistent homology with time-frequency representations, we capture multi-scale topological features that characterize the dynamic behavior of brain activity. This approach identifies 0D (connected components) and 1D (loops) topological structures in the signal's time-frequency domain, enabling robust extraction of features invariant to noise and temporal misalignments. The proposed method is demonstrated on resting-state functional magnetic resonance imaging (fMRI) data, showcasing its ability to discern critical topological patterns and provide insights into functional connectivity. This topological approach opens new avenues for analyzing complex brain signals, offering potential applications in neuroscience and clinical diagnostics.