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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.
Physical Review. E
|October 20, 2020
Summary
We developed a novel signal detection method that identifies unknown signals in any noise, even with infinite variance. This technique analyzes rank-time distributions to distinguish signals from noise, enabling efficient detection in single time series.
Area of Science:
- Data analysis
- Signal processing
- Statistical modeling
Background:
- Detecting unknown signals in noisy data is challenging.
- Traditional methods struggle with heavy-tailed noise and single time series.
- A robust method for signal-noise decomposition is needed.
Purpose of the Study:
- To introduce a simple and efficient method for detecting signals of unknown form.
- To enable signal detection in diverse noise conditions, including heavy-tailed noise.
- To provide a tool for analyzing single time series data.
Main Methods:
- Signal-noise decomposition based on rank and time.
- Analyzing the joint rank-time probability distribution of data.
- Utilizing rank-time cumulative distributions to capture signal-induced distortions.
Main Results:
- Stationary white noise exhibits a uniform rank-time probability distribution.
- Any signal, regardless of form, distorts this uniformity.
- The method allows for efficient detection of signals even in noise with infinite variance.
Conclusions:
- The proposed rank-time analysis offers a universal approach to signal detection.
- This method is effective for single time series and complex noise environments.
- It provides a robust tool for identifying subtle signals within noisy datasets.
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