Detection of unknown signals in arbitrary noise.

Abstract

We devise a simple method for detecting signals of unknown form buried in any noise, including heavy tailed. The method centers on signal-noise decomposition in rank and time: Only stationary white noise generates data with a jointly uniform rank-time probability distribution, U(1,N)×U(1,N), for N data points in a time series. Signals of any kind distort this uniformity. Such distortions are captured by rank-time cumulative distributions permitting all-purpose efficient detection, even for single time series and noise of infinite variance.