Beyond the Fourier Transform: Signal Symmetry Breaking in the Complex Plane

In this letter, we invert the ordinary point of view in the analysis of noisy data by treating the signal as a perturbation of the noise. The generating function of pure noise is represented, in the Complex Plane, by poles and zeros (Froissart doublets) having a universal, isotropic statistical distribution. The presence of a signal breaks this rotational symmetry. This allows to detect signals deeply embedded in noise that traditional methods cannot reach.