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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

1/f noise from the sequence of nonoverlapping rectangular pulses.

Aleksejus Kononovicius¹, Bronislovas Kaulakys¹

¹Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio 3, Vilnius LT-10257, Lithuania.

Physical Review. E

|April 19, 2023

Summary

Researchers found that 1/f noise appears at low frequencies in signals made of rectangular pulses. This occurs when pulse durations follow a power-law distribution and are longer than gaps.

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Area of Science:

Signal processing
Statistical physics
Noise analysis

Background:

Understanding the statistical properties of signals is crucial in various scientific fields.
Power spectral density (PSD) analysis is a key tool for characterizing signal behavior.
1/f noise, a ubiquitous phenomenon, has been observed in diverse systems.

Purpose of the Study:

To derive a general formula for the power spectral density (PSD) of signals composed of nonoverlapping rectangular pulses.
To analyze the conditions under which 1/f noise emerges in such signals.
To investigate the influence of pulse and gap duration distributions on the observed noise characteristics.

Main Methods:

Derivation of a general formula for the PSD of sequences of nonoverlapping pulses.
Detailed analysis of the specific case involving rectangular pulses.
Investigation of power-law distributions for pulse and gap durations.

Main Results:

A general formula for the PSD of nonoverlapping pulse sequences was derived.
Pure 1/f noise was shown to manifest at extremely low frequencies.
The emergence of 1/f noise is contingent upon specific relationships between pulse/gap durations and their power-law distribution.

Conclusions:

The study provides a theoretical framework for understanding 1/f noise in rectangular pulse signals.
Specific conditions regarding pulse/gap duration distributions are identified as critical for observing 1/f noise.
The findings are applicable to both ergodic and weakly nonergodic processes.