title: Cross-correlation of bio-signals using continuous wavelet transform and genetic algorithm.
abstract: 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.
  
  
  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.
  
  
  CONCLUSIONS
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Polish-Japanese Academy of Information Technology, Warsaw, Poland. Electronic address: piotrsukiennik@gmail.com.
authors.forename: Piotr
authors.initials: P
authors.lastname: Sukiennik
authors.affiliation: Polish-Japanese Academy of Information Technology, Warsaw, Poland and University of Colorado Denver, Denver, Colorado, USA.
authors.forename: Jan T
authors.initials: JT
authors.lastname: Białasiewicz
mesh_terms: D000465:Algorithms; D062186:Arterial Pressure / Q000502:physiology*; D004569:Electroencephalography / Q000706:statistics & numerical data*; D006801:Humans; D058067:Wavelet Analysis
keywords: Autocorrelation; Cross-correlation; Signal processing; Wavelet analysis