Cross-correlation of bio-signals using continuous wavelet transform and genetic algorithm

Background: Continuous wavelet transform allows to obtain time-frequency representation of a signal and analyze short-lived temporal interaction of concurrent processes. That offers good localization in both time and frequency domain. Scalogram and coscalogram analysis of two signal interaction dynamics gives an indication of the cross-correlation of analyzed signals in both domains.

New methods: We have used genetic algorithm with a fitness function based on signals convolution to find time delay between investigated signals. Two methods of cross-correlation are proposed: one that finds single delay for analyzed signals, and one returns a vector of delay values for each of wavelet transform sub-band center frequencies. Algorithms were implemented using MATLAB.

Results: We have extracted the data of simultaneously recorded encephalogram and arterial blood pressure and have investigated their interaction dynamics. We found time delay whose value cannot be precisely determined by scalograms and coscalogram inspection. The biomedical signals used come from MIMIC database.

Comparison with existing method(s): Cross-correlation of two complex signals is commonly performed using fast Fourier transform. It works well for signals with invariant frequency content. We have determined the time delay between analyzed signals using wavelet scalograms and we have accordingly shifted one of them, aligning associated events. Their coscalogram indicates the cross-correlation of the associated events.

Conclusion: Introducing new methods of wavelet transform in cross-correlation analysis has proven to be beneficial to the gain of the information about process interaction. Introduced solutions could be used to reason about causality between processes and gain bigger insight regarding analyzed systems.