319 research outputs found
Investigation of zero-crossings as information carriers
Analysis of bandlimited signal transmission by zero crossings of optimum signa
Average sampling of band-limited stochastic processes
We consider the problem of reconstructing a wide sense stationary
band-limited process from its local averages taken either at the Nyquist rate
or above. As a result, we obtain a sufficient condition under which average
sampling expansions hold in mean square and for almost all sample functions.
Truncation and aliasing errors of the expansion are also discussed
On causal extrapolation of sequences with applications to forecasting
The paper suggests a method of extrapolation of notion of one-sided
semi-infinite sequences representing traces of two-sided band-limited
sequences; this features ensure uniqueness of this extrapolation and
possibility to use this for forecasting. This lead to a forecasting method for
more general sequences without this feature based on minimization of the mean
square error between the observed path and a predicable sequence. These
procedure involves calculation of this predictable path; the procedure can be
interpreted as causal smoothing. The corresponding smoothed sequences allow
unique extrapolations to future times that can be interpreted as optimal
forecasts.Comment: arXiv admin note: substantial text overlap with arXiv:1111.670
Time shifted aliasing error upper bounds for truncated sampling cardinal series
AbstractTime shifted aliasing error upper bound extremals for the sampling reconstruction procedure are fully characterized. Sharp upper bounds are found on the aliasing error of truncated cardinal series and the corresponding extremals are described for entire functions from certain specific Lp, p>1, classes. Analogous results are obtained in multidimensional regular sampling. Truncation error analysis is provided in all cases considered. Moreover, sharpness of bounding inequalities, convergence rates and various sufficient conditions are discussed
Spatiospectral concentration of vector fields on a sphere
We construct spherical vector bases that are bandlimited and spatially
concentrated, or, alternatively, spacelimited and spectrally concentrated,
suitable for the analysis and representation of real-valued vector fields on
the surface of the unit sphere, as arises in the natural and biomedical
sciences, and engineering. Building on the original approach of Slepian,
Landau, and Pollak we concentrate the energy of our function bases into
arbitrarily shaped regions of interest on the sphere, and within certain
bandlimits in the vector spherical-harmonic domain. As with the concentration
problem for scalar functions on the sphere, which has been treated in detail
elsewhere, a Slepian vector basis can be constructed by solving a
finite-dimensional algebraic eigenvalue problem. The eigenvalue problem
decouples into separate problems for the radial and tangential components. For
regions with advanced symmetry such as polar caps, the spectral concentration
kernel matrix is very easily calculated and block-diagonal, lending itself to
efficient diagonalization. The number of spatiospectrally well-concentrated
vector fields is well estimated by a Shannon number that only depends on the
area of the target region and the maximal spherical-harmonic degree or
bandwidth. The spherical Slepian vector basis is doubly orthogonal, both over
the entire sphere and over the geographic target region. Like its scalar
counterparts it should be a powerful tool in the inversion, approximation and
extension of bandlimited fields on the sphere: vector fields such as gravity
and magnetism in the earth and planetary sciences, or electromagnetic fields in
optics, antenna theory and medical imaging.Comment: Submitted to Applied and Computational Harmonic Analysi
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