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From a time series whose data are embedded in heavy noise, we construct anHilbert space operator (J-operator) whose discrete spectrum represents thesignal while the essential spectrum located on the unit circle, is associatedwith the noise. Furthermore the essential spectrum, in the absence of signal,is built from roots of unity ("clock" distribution). These results areindependent of the statistical properties of the noise that can be Gaussian,non-Gaussian, pink or even without second moment (Levy). The presence of thesignal has for effect to break the clock angular distribution of the essentialspectrum on the unit circle. A discontinuity, proportional to the intensity ofthe signal, appears in the angular distribution. The sensitivity of this methodis definitely better than standard techniques. We build an example thatsupports our claims.

Signal induced Symmetry Breaking in Noise Statistical Properties of Data Analysis