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General mechanism for the 1/f noise.

Avinash Chand Yadav1, Ramakrishna Ramaswamy2, Deepak Dhar3

  • 1Department of Physics and Astronomical Sciences, Central University of Jammu, Samba 181 143, India.

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Summary

Nonlinear devices can transform input noise spectra. This study shows how nonlinear transformations tune output spectral indices, offering a general mechanism for ubiquitous 1/f noise in nature.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Signal Processing

Background:

  • 1/f noise, also known as pink noise, is prevalent in various natural systems.
  • Understanding the generation mechanisms of 1/f noise is crucial for diverse scientific fields.
  • Previous models often lack a generalizable explanation for the ubiquitous nature of 1/f noise.

Purpose of the Study:

  • To investigate the spectral modification of Gaussian noise by memoryless nonlinear devices.
  • To demonstrate a tunable mechanism for generating 1/f noise spectra.
  • To provide a general framework for explaining the widespread occurrence of 1/f noise.

Main Methods:

  • Analysis of the instantaneous response of memoryless nonlinear devices to input signals.
  • Mathematical modeling of the power spectrum transformation from input to output.
  • Characterization of the relationship between the nonlinear transformation and the output spectral index.

Main Results:

  • Input Gaussian noise with a power spectrum of 1/f^{α} is transformed into an output spectrum of 1/f^{α^{'}}, where α^{'} is generally not equal to α.
  • The modified spectral index α^{'} is dependent on the specific nonlinear transformation applied.
  • Continuous tuning of the spectral index α^{'} is achievable by altering the nonlinearity.

Conclusions:

  • Memoryless nonlinear devices provide a general mechanism for generating tunable 1/f noise.
  • The presented findings offer a unified explanation for the ubiquitous 1/f noise observed across natural phenomena.
  • This work opens avenues for controlling and understanding noise characteristics in complex systems.