The method in which the wavelet transform and fractal theories are applied to detect chaotic signals with the additive observed noises is presented in this paper. Smoothing operator is derived from wavelet transform and used to process the chaotic time series. According to its character of no-scale interval in certain scales, a detected example of the noisy chaotic behavior produced by a Lorenz attractor is provided by using the improved G-P algorithm to calculate its fractal dimension. The results shows that the method introduced here expresses a good ability to detect chaos.
"Detection of chaos based on wavelet transform", Proc. SPIE 2825, Wavelet Applications in Signal and Image Processing IV, (23 October 1996); doi: 10.1117/12.255303; https://doi.org/10.1117/12.255303