Nonlinear Analysis of Surface EMG Signals
Min Lei, Guang Meng · InTech eBooks · 2012
120 build on a broad and strong foundation of nonlinear time series analysis and chaotic dynamical theory. Surrogate data test methodSurrogate data method includes two parts: a null hypothesis and a test statistic.The null hypothesis is a specific process which may or may not adequately explain an origin of the data.The test statistic provides a quantitative description to demonstrate the data sources.Nonlinear Analysis of Surface EMG Signals 121 Null hypotheses and algorithms[1]The null hypotheses usually specify some certain properties of the original data that reflect some structure characteristics of the dynamical system, such as mean and variance, and possibly also the Fourier power spectrum.Different null hypotheses describe different specific dynamical systems.In terms of the corresponding null hypothesis, the surrogate data can be generated so as to test the corresponding specific dynamical system class. Null hypothesis 1The observed data is produced by independent and identically distributed (IID) random variables.For this hypothesis, the corresponding surrogate data can be generated by shuffling the time-order of the original time series so that it has the same mean, variance and amplitude distribution as the original data.But any temporal correlations of the original data are destroyed in the surrogate data.Schienkman and LeBaron[8] applied this hypothesis to analyze stock market returns.Breeden and Packard also used this hypothesis to demonstrate that a time series of quasar data which were sampled nonuniformly in time has some dynamics structure [9].The algorithm of the null hypothesis is that one first create gaussian random numbers from 1 to N, where N is the length of the original data x.Then, the original data x is permuted by the random numbers to generate the surrogate data. Null hypothesis 2The observed data is produced by the Ornstein-Uhlenbeck process.The surrogate data generated by the Ornstein-Uhlenbeck process is a sequence that has the simplest time correlation.The Ornstein-Uhlenbeck process can be given as follows.