Spectral analysis and generation of certain highly oscillatory curves related to chaos |
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| Authors: | Goong Chen Maria Christina Mariani Indranil SenGuptaNicholas Mai |
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| Institution: | a Mathematics Department and Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX 77843, United Statesb Science Program, Texas A&M University at Qatar, Doha, Qatarc Mathematical Science Department, University of Texas at El Paso, El Paso, TX 79968, United Statesd Mathematics and Electrical Engineering Departments, Texas A&M University, College Station, TX 77843, United States |
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| Abstract: | Highly oscillatory phenomena are omnipresent in applications. Two important underlying sources are stochastic fluctuations and deterministic randomness. In this paper, we will present heuristics, theorems, and a few illustrations on the Fourier spectrum and deterministic random time series, based upon our understanding of certain rapid oscillations in chaos. |
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| Keywords: | Highly oscillatory curves Oscillation and chaos Fourier analysis Wavelet Curve fitting |
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