Noise smoothing for nonlinear time series using wavelet soft threshold

In this letter, a new threshold algorithm based on wavelet analysis is applied to smooth noise for a nonlinear time series. By detailing the signals decomposed onto different scales, we smooth the details by using the updated thresholds to different characters of a noisy nonlinear signal. This method is an improvement of Donoho's wavelet methods to nonlinear signals. The approach has been successfully applied to smoothing the noisy chaotic time series generated by the Lorenz system as well as the observed annual runoff of Yellow River. For the nonlinear dynamical system, an attempt is made to analyze the noise reduced data by using multiresolution analysis, i.e., the false nearest neighbors, correlation integral, and autocorrelation function, to verify the proposed noise smoothing algorithm.