  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.
