11,277 research outputs found
Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples
This paper presents a novel power spectral density estimation technique for
band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The
technique employs multi-coset sampling and incorporates the advantages of
compressed sensing (CS) when the power spectrum is sparse, but applies to
sparse and nonsparse power spectra alike. The estimates are consistent
piecewise constant approximations whose resolutions (width of the piecewise
constant segments) are controlled by the periodicity of the multi-coset
sampling. We show that compressive estimates exhibit better tradeoffs among the
estimator's resolution, system complexity, and average sampling rate compared
to their noncompressive counterparts. For suitable sampling patterns,
noncompressive estimates are obtained as least squares solutions. Because of
the non-negativity of power spectra, compressive estimates can be computed by
seeking non-negative least squares solutions (provided appropriate sampling
patterns exist) instead of using standard CS recovery algorithms. This
flexibility suggests a reduction in computational overhead for systems
estimating both sparse and nonsparse power spectra because one algorithm can be
used to compute both compressive and noncompressive estimates.Comment: 26 pages, single spaced, 9 figure
Adaptive Graph Signal Processing: Algorithms and Optimal Sampling Strategies
The goal of this paper is to propose novel strategies for adaptive learning
of signals defined over graphs, which are observed over a (randomly
time-varying) subset of vertices. We recast two classical adaptive algorithms
in the graph signal processing framework, namely, the least mean squares (LMS)
and the recursive least squares (RLS) adaptive estimation strategies. For both
methods, a detailed mean-square analysis illustrates the effect of random
sampling on the adaptive reconstruction capability and the steady-state
performance. Then, several probabilistic sampling strategies are proposed to
design the sampling probability at each node in the graph, with the aim of
optimizing the tradeoff between steady-state performance, graph sampling rate,
and convergence rate of the adaptive algorithms. Finally, a distributed RLS
strategy is derived and is shown to be convergent to its centralized
counterpart. Numerical simulations carried out over both synthetic and real
data illustrate the good performance of the proposed sampling and
reconstruction strategies for (possibly distributed) adaptive learning of
signals defined over graphs.Comment: Submitted to IEEE Transactions on Signal Processing, September 201
Evaluating Maximum Likelihood Estimation Methods to Determine the Hurst Coefficient
A maximum likelihood estimation method implemented in S-PLUS (S-MLE) to estimate the Hurst coefficient (H) is evaluated. The Hurst coefficient, with 0.5\u3cHS-MLE was developed to estimate H for fractionally differenced (fd) processes. However, in practice it is difficult to distinguish between fd processes and fractional Gaussian noise (fGn) processes. Thus, the method is evaluated for estimating H for both fd and fGn processes. S-MLE gave biased results of H for fGn processes of any length and for fd processes of lengths less than 210. A modified method is proposed to correct for this bias. It gives reliable estimates of H for both fd and fGn processes of length greater than or equal to 211
A Statistical Inference Method for Interpreting the CLASP Observations
On 3rd September 2015, the Chromospheric Lyman-Alpha SpectroPolarimeter
(CLASP) successfully measured the linear polarization produced by scattering
processes in the hydrogen Lyman- line of the solar disk radiation,
revealing conspicuous spatial variations in the and signals. Via
the Hanle effect the line-center and amplitudes encode information
on the magnetic field of the chromosphere-corona transition region (TR), but
they are also sensitive to the three-dimensional structure of this corrugated
interface region. With the help of a simple line formation model, here we
propose a statistical inference method for interpreting the Lyman-
line-center polarization observed by CLASP.Comment: Accepted for publication in The Astrophysical Journa
Narrow-Angle Astrometry with the Space Interferometry Mission: The Search for Extra-Solar Planets. II. Detection and Characterization of Planetary Systems
(Abridged) The probability of detecting additional companions is essentially
unchanged with respect to the single-planet configurations, but after fitting
and subtraction of orbits with astrometric signal-to-noise ratio
the false detection rates can be enhanced by up to a
factor 2; the periodogram approach results in robust multiple-planet detection
for systems with periods shorter than the SIM mission length, even at low
values of , while the least squares technique combined with
Fourier series expansions is arguably preferable in the long-period regime. The
accuracy on multiple-planet orbit reconstruction and mass determination suffers
a typical degradation of 30-40% with respect to single-planet solutions; mass
and orbital inclination can be measured to better than 10% for periods as short
as 0.1 yr, and for as low as , while
is required in order to measure with similar
accuracy systems harboring objects with periods as long as three times the
mission duration. For systems with all components producing
or greater, quasi-coplanarity can be reliably
established with uncertainties of a few degrees, for periods in the range
yr; in systems where at least one component has
, coplanarity measurements are compromised, with typical
uncertainties on the mutual inclinations of order of . Our
findings are illustrative of the importance of the contribution SIM will make
to the fields of formation and evolution of planetary systems.Comment: 61 pages, 14 figures, 5 tables, to appear in the September 2003 Issue
of the Publications of the Astronomical Society of the Pacifi
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