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Detection of unknown signals in arbitrary noise
Glenn Ierley1, Alex Kostinski2
1Department of Mathematical Sciences, Michigan Technological University, Houghton, Michigan 49931, USA and Scripps Institution of Oceanography, University of California San Diego, San Diego, California 92093, USA.
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.
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