The discrete complex wavelet approach to phase assignment and a new test bed for related methods

Area of Science:

• Complex Systems Science
• Signal Processing
• Non-linear Dynamics

Background:

• Accurate phase assignment is crucial for understanding non-linear oscillator dynamics.
• Existing phase detection techniques struggle with observational noise and limited data.
• Experimental data often presents challenges for traditional phase analysis methods.

Purpose of the Study:

• To introduce a new phase assignment methodology for non-linear oscillators.
• To evaluate the accuracy and robustness of the proposed approach against noise and limited data.
• To compare the new method with existing phase detection techniques.

Main Methods:

• Development of the Discrete Complex Wavelet Approach (DCWA) based on the dual-tree complex wavelet transform.
• Creation of a specialized testbed generating time series data from non-linear oscillator-like dynamics with known theoretical phases.
• Numerical benchmarks to assess performance under various phase synchronization scenarios and noise levels.

Main Results:

• The DCWA accurately measures phase differences, tracking fine variations even with Gaussian noise.
• The method performs reliably when only a single scalar measure of the oscillator is available.
• Numerical benchmarks demonstrate DCWA's effectiveness, particularly in moderate to high noise environments, outperforming other methods.

Conclusions:

• The Discrete Complex Wavelet Approach offers a reliable and accurate method for phase assignment in non-linear oscillators.
• DCWA is particularly advantageous for analyzing experimental data due to its robustness against noise.
• This methodology provides a valuable tool for researchers in complex systems and non-linear dynamics.