680 research outputs found
Metrology and 1/f noise: linear regressions and confidence intervals in flicker noise context
1/f noise is very common but is difficult to handle in a metrological way.
After having recalled the main characteristics of stongly correlated noise,
this paper will determine relationships giving confidence intervals over the
arithmetic mean and the linear drift parameters. A complete example of
processing of an actual measurement sequence affected by 1/f noise will be
given
Non-equilibrium critical behavior : An extended irreversible thermodynamics approach
Critical phenomena in non-equilibrium systems have been studied by means of a
wide variety of theoretical and experimental approaches. Mode-coupling,
renormalization group, complex Lie algebras and diagrammatic techniques are
some of the usual theoretical tools. Experimental studies include light and
inelastic neutron scattering, X-ray photon correlation spectroscopy, microwave
interferometry and several other techniques. Nevertheless no conclusive
reatment has been developed from the basic principles of a thermodynamic theory
of irreversible processes. We have developed a formalism in which we obtain
correlation functions as field averages of the associated functions. By
applying such formalism we attempt to find out if the resulting correlation
functions will inherit the mathematical properties (integrability, generalized
homogeneity, scaling laws) of its parent potentials, and we will also use these
correlation functions to study the behavior of macroscopic systems far from
equilibrium, specially in the neighborhood of critical points or dynamic phase
transitions. As a working example we will consider the mono-critical behavior
of a non-equilibrium binary fluid mixture close to its consolute point.Comment: 23 pages, 3 figures, 1 tabl
The Omega Counter, a Frequency Counter Based on the Linear Regression
This article introduces the {\Omega} counter, a frequency counter -- or a
frequency-to-digital converter, in a different jargon -- based on the Linear
Regression (LR) algorithm on time stamps. We discuss the noise of the
electronics. We derive the statistical properties of the {\Omega} counter on
rigorous mathematical basis, including the weighted measure and the frequency
response. We describe an implementation based on a SoC, under test in our
laboratory, and we compare the {\Omega} counter to the traditional {\Pi} and
{\Lambda} counters. The LR exhibits optimum rejection of white phase noise,
superior to that of the {\Pi} and {\Lambda} counters. White noise is the major
practical problem of wideband digital electronics, both in the instrument
internal circuits and in the fast processes which we may want to measure. The
{\Omega} counter finds a natural application in the measurement of the
Parabolic Variance, described in the companion article arXiv:1506.00687
[physics.data-an].Comment: 8 pages, 6 figure, 2 table
The Parabolic variance (PVAR), a wavelet variance based on least-square fit
This article introduces the Parabolic Variance (PVAR), a wavelet variance
similar to the Allan variance, based on the Linear Regression (LR) of phase
data. The companion article arXiv:1506.05009 [physics.ins-det] details the
frequency counter, which implements the LR estimate.
The PVAR combines the advantages of AVAR and MVAR. PVAR is good for long-term
analysis because the wavelet spans over , the same of the AVAR wavelet;
and good for short-term analysis because the response to white and flicker PM
is and , same as the MVAR.
After setting the theoretical framework, we study the degrees of freedom and
the confidence interval for the most common noise types. Then, we focus on the
detection of a weak noise process at the transition - or corner - where a
faster process rolls off. This new perspective raises the question of which
variance detects the weak process with the shortest data record. Our
simulations show that PVAR is a fortunate tradeoff. PVAR is superior to MVAR in
all cases, exhibits the best ability to divide between fast noise phenomena (up
to flicker FM), and is almost as good as AVAR for the detection of random walk
and drift
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