Detection of a particular event with a known pattern in a noisy signal is the subject of this paper. The purpose is to compare three events detection methods based on matched filtering, decomposition in a set of orthonormal functions and wavelets analysis. The application which is considered here concerns K-complex detection in sleep EEG signals.I. INTRODUCTION The electrical activity of the human brain has been studied extensively since the discovery of the EEG by BERGER in 1924 [l]. In EEG analysis, K-complexes and spindles take a prominent part in sleep research and justify the development of detection methods for automatic recognition. Since a method for K-complex detection using fuzzy logic has been described previously [2], this paper focuses on K-complexes recognition in sleep EEG using methods based on a decomposition of the signal.
METHODSThe general idea is to make the projection of the signal x(t) on one or several elementary functions vi (t) which depend on one or several parameters. In this way we obtain a set of coefficients ci(t) which are then compared to reference parameters relative to the expected events.Decomposition of the signal is obtained using : m x(t) = C(ci(t)xvi(t)) (synthesis) where coefficients are computed in this manner: i=O m ci (t) = x(t). vi (t) . dt 0 Note : if the functions y~i(t) are orthogonal, then the coefficients ci( t) are independent.Three decomposition methods are considered in this paper:pi (T + t -Ti) .dT 0 where * denotes the convolution product and Ti is the duration of the event pi (t) to be detected.
Decomposition in a set of orthonomalfunctionsLet x(t) be a deterministic signal with finite energy, and observed over the interval t E [ti, tf 1, then an orthonormal set of functions {$i(t), i = l , 2, ...} is obtained by the Gram-Schmidt orthogonalization procedure [ 31. Then coefficient ci (t) are comnuted with :
Wavelets DecompositionWavelets analysis is obtain in this way : t ci(t)= x*y~2i (t)=jx(T).v2i(t-T).dT 0 where v2i (t) is the dilation by a factor 2' of a basic wavelet Y(t) proposed by Sdphane Mallat 141, VI.
