Surrogate analysis of coherent multichannel data

We present a method for generating surrogate data for multichannel time series. By preserving both the power spectra and the cross spectrum of the original data, we can determine if a given statistical test (such as the synchronization index) is being biased by the presence of coherence due to linear superposition of the separate measurements. Current methods based on phase randomization techniques are unsuitable for this particular task. This method is demonstrated on various canonical systems and numerical models. We will show that this algorithm is capable of properly preserving the power spectra and coherence function of the original data, and furthermore, that with the help of surrogate analysis the synchronization index measure is capable of distinguishing between coupled nonlinear oscillators and coherent superpositions of independent chaotic oscillators.