کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1895621 1533992 2016 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Wavelet shrinkage of a noisy dynamical system with non-linear noise impact
ترجمه فارسی عنوان
انقباض موجک یک سیستم دینامیکی پر سر و صدا با تاثیر نوری خطی
کلمات کلیدی
موجها، سیستم های دینامیک، آستانه، طراحی نامحدود تاثیر نوری خطی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی


• Wavelet shrinkage of a noisy chaos.
• Nonlinear noise influence and nonequispaced sample: a new kind of signal processing.
• Noise described by alpha-stable random variables.
• Robustness of the threshold filters to leptokurtic noise.
• Application to simulated logistic and Lorenz chaos and to financial data.

By filtering wavelet coefficients, it is possible to construct a good estimate of a pure signal from noisy data. Especially, for a simple linear noise influence, Donoho and Johnstone (1994) have already defined an optimal filter design in the sense of a minimization of the error made when estimating the pure signal. We set here a different framework where the influence of the noise is non-linear. In particular, we propose a method to filter the wavelet coefficients of a discrete dynamical system disrupted by a weak noise, in order to construct good estimates of the pure signal, including Bayes’ estimate, minimax estimate, oracular estimate or thresholding estimate. We present the example of a logistic and a Lorenz chaotic dynamical system as well as an adaptation of our technique in order to show empirically the robustness of the thresholding method in presence of leptokurtic noise. Moreover, we test both the hard and the soft thresholding and also another kind of smoother thresholding which seems to have almost the same reconstruction power as the hard thresholding. Finally, besides the tests on an estimated dataset, the method is tested on financial data: oil prices and NOK/USD exchange rate.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 325, 15 June 2016, Pages 126–145
نویسندگان
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