Windowing Compensation in Fourier Based Surrogate Analysis

This paper shows how adding a second step of windowing after each phase randomization can reduce the False Rejection Rate in Fourier based Surrogate Analysis. Windowing techniques improve the resolution of the Power Spectrum estimation by reducing the sampling gap caused by the periodic extension of the Fourier Series. However, it adds a time domain non-stationarity which affects the Surrogate Analysis. This effect is particularly problematic for short lowpass signals. Applying the same window to the surrogate data allows having the same non-stationarity. 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-sided 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 as well as bilateral tests.