178 research outputs found
A generalised Measurement Equation and van Cittert-Zernike theorem for wide-field radio astronomical interferometry
We derive a generalised van Cittert-Zernike (vC-Z) theorem for radio
astronomy that is valid for partially polarized sources over an arbitrarily
wide field-of-view (FoV). The classical vC-Z theorem is the theoretical
foundation of radio astronomical interferometry, and its application is the
basis of interferometric imaging. Existing generalised vC-Z theorems in radio
astronomy assume, however, either paraxiality (narrow FoV) or scalar
(unpolarized) sources. Our theorem uses neither of these assumptions, which are
seldom fulfilled in practice in radio astronomy, and treats the full
electromagnetic field. To handle wide, partially polarized fields, we extend
the two-dimensional electric field (Jones vector) formalism of the standard
"Measurement Equation" of radio astronomical interferometry to the full
three-dimensional formalism developed in optical coherence theory. The
resulting vC-Z theorem enables all-sky imaging in a single telescope pointing,
and imaging using not only standard dual-polarized interferometers (that
measure 2-D electric fields), but also electric tripoles and electromagnetic
vector-sensor interferometers. We show that the standard 2-D Measurement
Equation is easily obtained from our formalism in the case of dual-polarized
antenna element interferometers. We find, however, that such dual-polarized
interferometers can have polarimetric aberrations at the edges of the FoV that
are often correctable. Our theorem is particularly relevant to proposed and
recently developed wide FoV interferometers such as LOFAR and SKA, for which
direction-dependent effects will be important.Comment: To be published in MNRA
Sampling errors of correlograms with and without sample mean removal for higher-order complex white noise with arbitrary mean
We derive the bias, variance, covariance, and mean square error of the
standard lag windowed correlogram estimator both with and without sample mean
removal for complex white noise with an arbitrary mean. We find that the
arbitrary mean introduces lag dependent covariance between different lags of
the correlogram estimates in spite of the lack of covariance in white noise for
non-zeros lags. We provide a heuristic rule for when the sample mean should be,
and when it should not be, removed if the true mean is not known. The sampling
properties derived here are useful is assesing the general statistical
performance of autocovariance and autocorrelation estimators in different
parameter regimes. Alternatively, the sampling properties could be used as
bounds on the detection of a weak signal in general white noise.Comment: 11 pages, 2 figures, To be published in Journal of Time Series
Analysi
Deriving the sampling errors of correlograms for general white noise
We derive the second-order sampling properties of certain autocovariance and
autocorrelation estimators for sequences of independent and identically
distributed samples. Specifically, the estimators we consider are the classic
lag windowed correlogram, the correlogram with subtracted sample mean, and the
fixed-length summation correlogram. For each correlogram we derive explicit
formulas for the bias, covariance, mean square error and consistency for
generalised higher-order white noise sequences. In particular, this class of
sequences may have non-zero means, be complexed valued and also includes
non-analytical noise signals. We find that these commonly used correlograms
exhibit lag dependent covariance despite the fact that these processes are
white and hence by definition do not depend on lag.Comment: Submitted to Biometrik
On the similarity of Information Energy to Dark Energy
Information energy is shown here to have properties similar to those of dark
energy. The energy associated with each information bit of the universe is
found to be defined identically to the characteristic energy of a cosmological
constant. Two independent methods are used to estimate the universe information
content of ~10^91 bits, a value that provides an information energy total
comparable to that of the dark energy. Information energy is also found to have
a significantly negative equation of state parameter, w < -0.4, and thus exerts
a negative pressure, similar to dark energy.Comment: 5 pages, no figures, no table
Instantaneous local wave vector estimation from multi-spacecraft measurements using few spatial points
Statistical properties of ionospheric stimulated electromagnetic emissions
We have analysed the statistical properties of the stimulated electromagnetic emissions (SEE) spectral features in the steady state, reached after a long period of continuous HF pumping of the ionosphere in experiments performed at the Sura ionospheric radio research facility in Russia. Using a digital filter bank method, we have been able to analyse complex valued signals within narrow frequency bands. Each of the SEE spectral features are thereby separated into a number of narrow spectral components. Statistical tests were performed for all these spectral components and the distributions of the spectral amplitudes and phases were evaluated. Also, a test for sinusoidal components was performed. These tests showed that all observed SEE features were indistinguishable from coloured Gaussian noise. The test results exclude that the SEE features can be the result of a single isolated coherent process, but does not rule out that there could be many statistically independent parametric wave-wave processes taking place simultaneously at various parts of the HF-pumped ionosphere, as long as the superposition from all these is incoherent. Furthermore, from the test results, we cannot exclude the possibility that the waveforms of some, or all, of the SEE features may be chaotic
Utilization of photon orbital angular momentum in the low-frequency radio domain
We show numerically that vector antenna arrays can generate radio beams which
exhibit spin and orbital angular momentum characteristics similar to those of
helical Laguerre-Gauss laser beams in paraxial optics. For low frequencies (< 1
GHz), digital techniques can be used to coherently measure the instantaneous,
local field vectors and to manipulate them in software. This opens up for new
types of experiments that go beyond those currently possible to perform in
optics, for information-rich radio physics applications such as radio
astronomy, and for novel wireless communication concepts.Comment: 4 pages, 5 figures. Changed title, identical to the paper published
in PR
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