Smoothing Chaotic Signals for System Identification: A Multiresolution Wavelet Decomposition Approach

A new wavelet based smoothing algorithm is introduced to reduce the noise affecting chaotic signals prior to system identification. The algorithm involves a miltiresolution decomposition of the signal using B-spline wavelets which makes use of the mutual information between neighbouring points in time. Rigorous results concerning the effects of noise on the wavelet coefficients and the efficiency of the smoothing procedure are derived. Noise corrupted signals generated from Chua's circuit and the Lorenz equation are used to test the new method. The correlation dimension and the largest Lyapunov exponent of the models, estimated using the smoothed signals, are compared with the true values to demonstrate that the new algorithm preserves the dynamical properties of the underlying system.