Signal induced Symmetry Breaking in Noise Statistical Properties of Data Analysis

Autor:	Perotti, Luca, Vrinceanu, Daniel, Bessis, Daniel
Rok vydání:	2010
Předmět:	Physics - Data Analysis Statistics and Probability
Druh dokumentu:	Working Paper
Popis:	From a time series whose data are embedded in heavy noise, we construct an Hilbert space operator (J-operator) whose discrete spectrum represents the signal while the essential spectrum located on the unit circle, is associated with the noise. Furthermore the essential spectrum, in the absence of signal, is built from roots of unity ("clock" distribution). These results are independent of the statistical properties of the noise that can be Gaussian, non-Gaussian, pink or even without second moment (Levy). The presence of the signal has for effect to break the clock angular distribution of the essential spectrum on the unit circle. A discontinuity, proportional to the intensity of the signal, appears in the angular distribution. The sensitivity of this method is definitely better than standard techniques. We build an example that supports our claims. Comment: 7 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1009.6021 Zobrazit plný text záznamu View this record from Arxiv