Related papers: Predicting the variance of a measurement with 1/f …
In this brief paper, we present a simple approach to estimate the variance of measurement noise with time-varying 1-D signals. The proposed approach exploits the relationship between the noise variance and the variance of the prediction…
A shear flow of liquid metal (Galinstan) is driven in an annular channel by counter-rotating traveling magnetic fields imposed at the endcaps. When the traveling velocities are large, the flow is turbulent and its azimuthal component…
To understand the sample-to-sample fluctuations in disorder-generated multifractal patterns we investigate analytically as well as numerically the statistics of high values of the simplest model - the ideal periodic $1/f$ Gaussian noise. By…
Noise of stochastic processes whose power spectrum scales at low frequencies, $f$, as $1/f$ appears in such diverse systems that it is considered universal. However, there have been a small number of instances from completely unrelated…
Consider a measurement in which the current coming out of a mesoscopic sample is filtered around a given frequency, amplified, measured and squared. Then this process is repeated many times and the results are averaged. Often, two such…
It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the behavior of the power spectrum of the excitation energy fluctuations, which is…
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…
There are several mathematical models yielding 1/f noise. For example, 1/f spectrum can be obtained from stochastic sequence of pulses having power-law distribution of pulse durations or from nonlinear stochastic differential equations. We…
Fluctuations of the electromagnetic field produced by quantized matter in external electric field are investigated. A general expression for the power spectrum of fluctuations is derived within the long-range expansion. It is found that in…
When the rate of shot noise is controlled by on-off states we speak of intermittent shot noise. The on-off states lead to alternately occurring clusters of events and intermissions, respectively. We derive the power spectrum of the…
The instability of an atomic clock is characterized by the Allan variance, a measure widely used to describe the noise of frequency standards. We provide an explicit method to find the ultimate bound on the Allan variance of an atomic clock…
We demonstrate that the measurement of $1/f^{\alpha}$ noise at the single molecule or nano-object limit is remarkably distinct from the macroscopic measurement over a large sample. The single particle measurements yield a conditional…
The traditional measurement theory interprets the variance as the dispersion of a measured value, which is actually contrary to a general mathematical concept that the variance of a constant is 0. This paper will fully demonstrate that the…
We consider the motion of a quantum particle whose position is measured in random places at random moments in time. We contrast this motion with the motion of a quantum particle in a potential which varies randomly in space and in time,…
This report describes a method for the primary calibration of phase noise and amplitude noise measurement systems. In the field of metrology, the term "primary" refers to a standard whose quantity value and measurement uncertainty are…
As a consequence of a general trend in the physics of oscillators and clocks towards optics, phase and frequency metrology is rapidly moving to optics too. Yet, optics is not replacing the traditional radio-frequency (RF) and microwave…
Starting from the simple point process model of 1/f noise we derive a stochastic nonlinear differential equation for the signal exhibiting 1/f noise in any desirably wide range of frequency. A stochastic differential equation (the general…
Fluctuation-enhanced sensing comprises the analysis of the stochastic component of the sensor signal and the utilization of the microscopic dynamics of the interaction between the agent and the sensor. We study the relationship between the…
Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent…
The vast majority of sampling systems operate in a standard way: at each tick of a fixed-frequency master clock a digitizer reads out a voltage that corresponds to the value of some physical quantity and translates it into a bit pattern…