Noise Smoothing for Nonlinear Time Series Using Wavelet Soft Threshold

• Published in: IEEE signal processing letters Vol. 14; no. 1; pp. 62 - 65
• Main Authors: Han, Min, Liu, Yuhua, Xi, Jianhui, Guo, Wei
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2007; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Chaos; Dynamical systems; Multiresolution analysis; Noise; Noise generators; Noise reduction; noise smoothing; Nonlinear dynamical systems; nonlinear time series; Nonlinearity; Rivers; Smoothing; Smoothing methods; soft threshold; Thresholds; Time series; Time series analysis; Wavelet; Wavelet analysis
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2006.881518

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