Windowing Compensation in Fourier Based Surrogate Analysis and Application to EEG Signal Classification

This article shows how adding a second step of windowing after each phase randomization can reduce the false rejection rate in the Fourier-based surrogate analysis (SA). Windowing techniques reduce the discontinuities at the boundaries of the periodically extended data sequence in the Fourier Series. However, they add time-domain nonstationarity that affects the SA. This effect is particularly problematic for short low-pass signals. Applying the same window to the surrogate data allows having the same nonstationarity. The method is tested on order 1 autoregressive process null hypothesis by Monte Carlo simulations. Previous methods were not able to yield good performances for left- and right-sided tests at the same time, even less with bilateral tests. It is shown that the new method is conservative for unilateral tests and bilateral tests. In order to show that the proposed windowing method can be useful in the real context, in this extended paper, it was applied for an electroencephalogram (EEG) diagnostic problem. A dataset comprising the EEG measurements of 15 subjects distributed in three groups, attention-deficit disorder primarily hyperactive-impulsive (ADHD), attention-deficit disorder primarily inattentive (ADD), and anxiety with attentional fragility (ANX), was used. Both statistical and machine learning (naive Bayesian) approaches were considered. The mean short-windowed SA (MSWSA) was used as a signal feature, and its performances were studied with respect to the windowing systems. The main findings were that: 1) the MSWSA feature has less variability for ADD than for ADHD or ANX; 2) the proposed windowing method reduces bias and nonnormality of the SA feature; 3) with the proposed method and a naive Bayesian classifier, a 93% success rate of discriminating ADD from ADHD and ANX was achieved with leave-one-out cross-validation; and 4) the new feature could not have yielded interesting results without the proposed windowing system.