Zhou, Cangtao; Cai, Tianxing; Heng Lai, Choy; Wang, Xingang; Lai, Ying-Cheng Model-based detector and extraction of weak signal frequencies from chaotic data. (English) Zbl 1306.37093 Chaos 18, No. 1, 013104, 12 p. (2008). Summary: Detecting a weak signal from chaotic time series is of general interest in science and engineering. In this work we introduce and investigate a signal detection algorithm for which chaos theory, nonlinear dynamical reconstruction techniques, neural networks, and time-frequency analysis are put together in a synergistic manner. By applying the scheme to numerical simulation and different experimental measurement data sets (Hénon map, chaotic circuit, and NH\(_3\) laser data sets), we demonstrate that weak signals hidden beneath the noise floor can be detected by using a model-based detector. Particularly, the signal frequencies can be extracted accurately in the time-frequency space. By comparing the model-based method with the standard denoising wavelet technique as well as supervised principal components analysis detector, we further show that the nonlinear dynamics and neural network-based approach performs better in extracting frequencies of weak signals hidden in chaotic time series.{©2008 American Institute of Physics} Cited in 3 Documents MSC: 37M10 Time series analysis of dynamical systems 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics 34C28 Complex behavior and chaotic systems of ordinary differential equations Software:Wavelet Toolbox PDFBibTeX XMLCite \textit{C. Zhou} et al., Chaos 18, No. 1, 013104, 12 p. (2008; Zbl 1306.37093) Full Text: DOI Link References: [1] DOI: 10.1016/0167-2789(86)90031-X · Zbl 0603.58040 · doi:10.1016/0167-2789(86)90031-X [2] DOI: 10.1016/0167-2789(94)00196-W · Zbl 0888.58031 · doi:10.1016/0167-2789(94)00196-W [3] DOI: 10.1016/0167-2789(95)00218-9 · Zbl 0890.94009 · doi:10.1016/0167-2789(95)00218-9 [4] DOI: 10.1103/PhysRevE.52.3420 · doi:10.1103/PhysRevE.52.3420 [5] DOI: 10.1063/1.2430294 · Zbl 1159.37378 · doi:10.1063/1.2430294 [6] DOI: 10.1103/PhysRevE.69.017201 · doi:10.1103/PhysRevE.69.017201 [7] DOI: 10.1103/PhysRevE.64.026221 · doi:10.1103/PhysRevE.64.026221 [8] DOI: 10.1109/5.362751 · doi:10.1109/5.362751 [9] DOI: 10.1109/78.782193 · Zbl 0979.94025 · doi:10.1109/78.782193 [10] DOI: 10.1109/78.600003 · doi:10.1109/78.600003 [11] DOI: 10.1103/PhysRevLett.98.108102 · doi:10.1103/PhysRevLett.98.108102 [12] DOI: 10.1063/1.2424423 · Zbl 1159.37377 · doi:10.1063/1.2424423 [13] DOI: 10.1103/PhysRevE.73.026214 · doi:10.1103/PhysRevE.73.026214 [14] DOI: 10.1063/1.2437579 · Zbl 1159.37409 · doi:10.1063/1.2437579 [15] DOI: 10.1063/1.2384909 · Zbl 1146.93380 · doi:10.1063/1.2384909 [16] DOI: 10.1238/Physica.Regular.065a00469 · Zbl 1062.37511 · doi:10.1238/Physica.Regular.065a00469 [17] DOI: 10.1238/Physica.Regular.065a00469 · Zbl 1062.37511 · doi:10.1238/Physica.Regular.065a00469 [18] Fukunaga K., Introduction to Statistical Pattern Recognition, 2. ed. (1990) · Zbl 0711.62052 [19] DOI: 10.1007/BFb0091924 · doi:10.1007/BFb0091924 [20] Kantz H., Nonlinear Time Series Analysis (1997) · Zbl 0873.62085 [21] Haykin S., Neural Networks, A Comprehensive Foundation (1999) · Zbl 0934.68076 [22] DOI: 10.1109/5.30749 · doi:10.1109/5.30749 [23] DOI: 10.1238/Physica.Regular.060a00300 · doi:10.1238/Physica.Regular.060a00300 [24] DOI: 10.1162/neco.1995.7.3.606 · doi:10.1162/neco.1995.7.3.606 [25] DOI: 10.1088/0031-8949/53/1/015 · doi:10.1088/0031-8949/53/1/015 [26] DOI: 10.1063/1.531938 · Zbl 0897.76038 · doi:10.1063/1.531938 [27] DOI: 10.1238/Physica.Regular.065a00025 · Zbl 1064.34514 · doi:10.1238/Physica.Regular.065a00025 [28] Misiti M., Wavelet Toolbox: For Use With Matlab® (1996) [29] DOI: 10.1103/PhysRevE.50.1874 · doi:10.1103/PhysRevE.50.1874 [30] DOI: 10.1103/PhysRevE.65.035204 · doi:10.1103/PhysRevE.65.035204 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.