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

Abstract

We analyze the power spectral density of a signal composed of nonoverlapping rectangular pulses. First, we derive a general formula for the power spectral density of a signal constructed from the sequence of nonoverlapping pulses. Then we perform a detailed analysis of the rectangular pulse case. We show that pure $1/f$ noise can be observed until extremely low frequencies when the characteristic pulse (or gap) duration is long in comparison to the characteristic gap (or pulse) duration, and gap (or pulse) durations are power-law distributed. The obtained results hold for the ergodic and weakly nonergodic processes.

arXiv comment14 pages, 5 figures

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Cited by in corpus (4)

• $1/f$ noise in semiconductors arising from the heterogeneous detrapping process of individual charge carriers
• Intermittent shot noise generating 1/f fluctuations
• Immediate recapture in the trapping-detrapping process of a single charge carrier
• Long-range correlations with finite-size effects from a superposition of uncorrelated pulses with power-law distributed durations