Tham khảo tài liệu 'recent advances in biomedical engineering 2011 part 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Linear and Nonlinear Synchronization Analysis and Visualization during Altered States of Consciousness 509 surrogate data has the same linear characteristics power spectrum and coherence as the experimental data but is otherwise random. In practice a set of p time series surrogates is constructed which share the same characteristics but lack the property we want to test the nonlinearity in our case. Using the newly created surrogates the same index Qsurrogates is repeatedly calculated leading to p 1 estimations of this. This procedure allows testing of the null hypothesis H0 that the original value of the statistic belongs to the distribution of the surrogates hence H0 is true. In other words one has to determine whether H0 can be rejected at the desired level of confidence. By estimating the mean and the standard deviation of the distribution of the statistic from the surrogates and then comparing them with its value from the original signals Z-score is calculated Q I surrogates Z 32 Ơ surrogates Z-score reveals the number of standard deviations Q is away from the mean Qs of the surrogates. Assuming that Q is approximately normally distributed in the surrogates ensemble H0 is rejected at the p significance level when Z one-sided test . If in addition no other possible causes of such a result can be accounted for then it is reasonable to conclude that the tested measure accounts for any nonlinear phenomena. However it should be noted that although the above surrogating procedure preserves both the autocorrelation of the signals and their linear cross-correlation the nonlinear individual structure of the individual signals if any is also destroyed. In other words any nonlinearity not only between but also within the signals is not present in the surrogates. Therefore these surrogates only test the hypothesis that the data are bivariate stochastic time series with an arbitrary degree of linear auto and cross-correlation Andrzejak Kraskov et al. 2003 . .
