J. Biomedical Science and Engineering, 2009, 2, 294-303 doi: 10.4236/jbise.2009.25044 Published Online September 2009 (http://www.SciRP.org/journal/jbise/ JBiSE ). Published Online September 2009 in SciRes. http://www.scirp.org/journal/jbise Sleep spindles detection from human sleep EEG signals using autoregressive (AR) model: a surrogate data approach Venkatakrishnan Perumalsamy 1 , Sangeetha Sankaranarayanan 2 , Sukanesh Rajamony 3 1 Department of Information Technology, Thiagarajar College of Engineering, Madurai, India; 2 Department of Electrical and Elec- tronics Engineering, Sethu Instituite of Technology, Madurai, India; 3 Department of Electronics and Communication Engineering, Thiagarajar College of Engineering, Madurai, India. Email: pvkit@tce.edu ; viggee_tce2000@yahoo.co.in ; rshece@tce.edu Received 5 May 2009; revised 19 July 2009; accepted 29 July 2009. ABSTRACT A new algorithm for the detection of sleep spindles from human sleep EEG with surrogate data approach is presented. Surrogate data ap- proach is the state of the art technique for nonlinear spectral analysis. In this paper, by developing autoregressive (AR) models on short segment of the EEG is described as a superposition of harmonic oscillating with damping and frequency in time. Sleep spindle events are detected, whenever the damping of one or more frequencies falls below a prede- fined threshold. Based on a surrogate data, a method was proposed to test the hypothesis that the original data were generated by a linear Gaussian process. This method was tested on human sleep EEG signal. The algorithm work well for the detection of sleep spindles and in addition the analysis reveals the alpha and beta band activities in EEG. The rigorous statistical framework proves essential in establishing these results. Keywords: AR Model; LPC; Sleep Spindles; Sur- rogate Data 1. INTRODUCTION Oscillatory signal activities are ubiquitous in the bio- medical signals [1]. Multielectrode recordings provide the opportunity to study signal oscillations from a net- work perspective. To assess signal interactions in the frequency domain, one often applies methods, such as ordinary coherence and Granger causality spectra [2] that are formulated within the frame work of linear sto- chastic process. Electroencephalogram (EEG) is one of the most important electrophysiological techniques used in human clinical and basic sleep research. In 1979 Bar- low proposed linear modeling system which has a long- lasting history in EEG analysis [3]. The models are mainly considered as a mathematical description of the signal and less as a biophysical model of the underlying neuronal mechanisms. In 1985, Frannaszczua et al. [4] proposed a model to interpret linear models as damped harmonic oscillators generating EEG activity based on the equivalence be- tween stochastically driven harmonic oscillators and autoregressive (AR) models. There is a unique transfor- mation between the AR coefficients and the frequencies and damping coefficients of the corresponding oscilla- tors. In particular at times when the EEG is dominated by a certain rhythmic activity e.g. in the case of sleep spindles or alpha activity, on might expect, that this ac- tivity will be rejected by a pole with a corresponding frequency and low damping. This idea was the staring point of our analysis [5]. The sleep EEG is always not stationary. However, we demonstrated that the effects of non stationary become relevant only with scales longer than 1s [6]. Therefore, short segments with duration of around 1s are suffi- ciently described by linear models. The non stationary in longer time scales might be rejected by the variation of the AR-coefficients and thus by the corresponding fre- quencies and damping coefficients. Based on the above considerations we propose an easy way to define oscil- latory events. They are detected, whenever the damping of one of the poles of a 1s AR model is below a prede- fined threshold. The method of surrogate data is a tool to test whether data were generated by some class of model. In 1992 the method of surrogate data proposed by Theiler et al. [7] is a general procedure to test whether data are consistent with some class of models. In order to test the hypothesis that the data are consistent with being generated by a linear system, the Fourier Transform (FT) algorithm is applied. Based on a example and the theory of linear stochastic systems we will show that this algorithm produce correct