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Aging Wiener-Khinchin Theorem
1Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel.
Physical Review Letters
|September 5, 2015
Summary
This study extends the Wiener-Khinchin theorem to analyze nonstationary random signals with aging correlations. It introduces two new theorems linking power spectra to correlation functions, revealing 1/f-type spectra from nonanalytical scaling functions.
Area of Science:
- Statistical physics
- Signal processing
- Complex systems
Background:
- The Wiener-Khinchin theorem connects the power spectrum and correlation function for stationary random signals.
- Nonstationary processes with aging correlations are common in nature but less understood theoretically.
- Existing methods struggle to analyze the spectral properties of these complex systems.
Purpose of the Study:
- To generalize the Wiener-Khinchin theorem for nonstationary processes with aging correlations.
- To establish a theoretical framework for relating power spectra to correlation functions in aging systems.
- To identify conditions leading to 1/f-type spectra in these systems.
Main Methods:
- Formulation of two novel aging Wiener-Khinchin theorems.
- Analysis of the relationship between power spectrum and time/ensemble-averaged correlation functions.
- Investigation of scaling functions exhibiting nonanalytical behavior.
Main Results:
- Two aging Wiener-Khinchin theorems are proposed, offering different analytical advantages.
- Nonanalytical behavior in the scaling function predicts aging 1/f-type spectra.
- The framework is validated using examples like blinking quantum dots and diffusion processes.
Conclusions:
- The developed aging Wiener-Khinchin theorems provide a powerful tool for analyzing nonstationary signals.
- The study clarifies the origin of 1/f-type spectra in various physical systems.
- The approach demonstrates broad applicability across diverse scientific mechanisms.
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