Reduction of noise in chaotic systems by wavelet multiscaling decomposition algorithm

We apply the wavelet multiscaling decomposition algorithm, which has been developed for noise reduction, to the extraction of periodic signal, noise and other chaotic signal from chaotic background. This algorithm utilizes the characteristic that wavelet transform has an outstanding local feature in time-frequency domains and it is a linear transform. Therefore it can distinguishes signals with different scales. In contrast to the previous methods our method uses the feature of signal scales and dose not demand restrictive assumptions that we must know the mathematical model of the chaotic background and that the amplitude of signal is smaller than that of the chaotic background. The results of computer simulation are given for extracting the sine signal, white noises (distributed uniformly or in Gaussion shape) and Chua's chaotic signal from Lorenz chaotic background.