Title :
Beyond the Fourier Transform: Signal Symmetry Breaking in the Complex Plane
Author :
Perotti, L. ; Vrinceanu, D. ; Bessis, D.
Author_Institution :
Dept. of Phys., Texas Southern Univ., Houston, TX, USA
Abstract :
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.
Keywords :
Fourier transforms; signal processing; statistical analysis; Fourier transform; Froissart doublets; complex plane; noisy data analysis; perturbation; poles and zeros; signal symmetry breaking; universal isotropic statistical distribution; Approximation methods; Fourier transforms; Noise; Oscillators; Poles and zeros; Statistical distributions; Time series analysis; Data analysis; noise; statistical distribution;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2012.2224864
