The effect of noise and nonlinear noise reduction methods on the fractal dimension of chaotic time series

Fractals ◽  
2021 ◽  
Author(s):  
Nazanin Zandi-Mehran ◽  
Sajad Jafari ◽  
Seyed Mohammad Reza Hashemi Golpayegani ◽  
Hamidreza Namazi
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Noise Reduction ◽  
Chaotic Time Series ◽  
Reduction Methods ◽  
Nonlinear Noise

Nonlinear noise reduction of chaotic time series based on multidimensional recurrent LS-SVM

2008 ◽  
Vol 71 (16-18) ◽  
pp. 3675-3679 ◽  
Author(s):  
Jiancheng Sun ◽  
Chongxun Zheng ◽  
Yatong Zhou ◽  
Yaohui Bai ◽  
Jianguo Luo
Keyword(s):  
Time Series ◽  
Noise Reduction ◽  
Chaotic Time Series ◽  
Nonlinear Noise

Noise reduction in chaotic time series data

Pramana ◽  
1999 ◽  
Vol 52 (1) ◽  
pp. 25-37 ◽  
Author(s):  
A. Bhowal ◽  
T. K. Roy
Keyword(s):  
Time Series ◽  
Noise Reduction ◽  
Time Series Data ◽  
Chaotic Time Series ◽  
Series Data

Smooth Projective Nonlinear Noise Reduction

2013 ◽  
Author(s):  
David Chelidze
Keyword(s):  
Time Series ◽  
Noise Reduction ◽  
Broad Spectrum ◽  
Reduction Method ◽  
Orthogonal Decomposition ◽  
Topological Properties ◽  
Noisy Time Series ◽  
Nonlinear Noise ◽  
Proper Orthogonal ◽  
Smooth Orthogonal Decomposition

Many nonlinear or chaotic time series exhibit an innate broad spectrum, which makes noise reduction difficult. Locally projective noise reduction is one of the most effective tools. It is based on proper orthogonal decomposition (POD), and works for both map-like and continuously sampled time series. However, POD only looks at geometrical or topological properties of data and does not take into account the temporal characteristics of time series. Here we present a new smooth projective noise reduction method. It uses bundles of locally reconstructed trajectory strands and their smooth orthogonal decomposition (SOD) to identify smooth local subspaces. Restricting trajectories to these subspaces imposes temporal smoothness on the filtered time series. It is shown that SOD-based noise reduction significantly outperforms the POD-based method for continuously sampled noisy time series.

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