Synchronization Analysis Module

The Synchronization Module quantifies temporal coordination between multiple participants, body segments, or movement components.
It provides methods to assess how well different movement signals align in time and phase.

Note

The method assumes stationarity over the analysis window and Gaussian noise.

Algorithms Details

Phase Coupling Analysis

Phase synchronization measures temporal alignment independent of amplitude:

1. Hilbert Transform: Compute analytic signals

\[ z_x(t) = x(t) + i H[x(t)], \quad z_y(t) = y(t) + i H[y(t)] \]

1. Instantaneous Phases:

\[ \phi_x(t) = \arg(z_x(t)), \quad \phi_y(t) = \arg(z_y(t)) \]

1. Phase Difference:

\[ \Delta \phi(t) = \phi_x(t) - \phi_y(t) \]

1. Phase Locking Value (PLV):

\[ \text{PLV} = \left| \frac{1}{N} \sum_{t=1}^{N} e^{i \Delta \phi(t)} \right| \]

Output: \( \text{PLV} \in [0,1] \)

Interpretation

• \( PLV > 0.7 \): strong phase coupling
• \( 0.4 < PLV \leq 0.7 \): moderate phase coupling
• \( PLV \leq 0.4 \): weak phase coupling

References

To be added