159 research outputs found
Orthonormal sequences in and time frequency localization
We study uncertainty principles for orthonormal bases and sequences in
. As in the classical Heisenberg inequality we focus on the product
of the dispersions of a function and its Fourier transform. In particular we
prove that there is no orthonormal basis for for which the time and
frequency means as well as the product of dispersions are uniformly bounded.
The problem is related to recent results of J. Benedetto, A. Powell, and Ph.
Jaming.
Our main tool is a time frequency localization inequality for orthonormal
sequences in . It has various other applications.Comment: 18 page
Dispersive estimates for Schr\"odinger operators with point interactions in
The study of dispersive properties of Schr\"odinger operators with point
interactions is a fundamental tool for understanding the behavior of many body
quantum systems interacting with very short range potential, whose dynamics can
be approximated by non linear Schr\"odinger equations with singular
interactions. In this work we proved that, in the case of one point interaction
in , the perturbed Laplacian satisfies the same
estimates of the free Laplacian in the smaller regime . These
estimates are implied by a recent result concerning the boundedness of
the wave operators for the perturbed Laplacian. Our approach, however, is more
direct and relatively simple, and could potentially be useful to prove optimal
weighted estimates also in the regime .Comment: To appear on: "Advances in Quantum Mechanics: Contemporary Trends and
Open Problems", G. Dell'Antonio and A. Michelangeli eds., Springer-INdAM
series 201
Quantization and Compressive Sensing
Quantization is an essential step in digitizing signals, and, therefore, an
indispensable component of any modern acquisition system. This book chapter
explores the interaction of quantization and compressive sensing and examines
practical quantization strategies for compressive acquisition systems.
Specifically, we first provide a brief overview of quantization and examine
fundamental performance bounds applicable to any quantization approach. Next,
we consider several forms of scalar quantizers, namely uniform, non-uniform,
and 1-bit. We provide performance bounds and fundamental analysis, as well as
practical quantizer designs and reconstruction algorithms that account for
quantization. Furthermore, we provide an overview of Sigma-Delta
() quantization in the compressed sensing context, and also
discuss implementation issues, recovery algorithms and performance bounds. As
we demonstrate, proper accounting for quantization and careful quantizer design
has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing
and Its Applications", 201
Frame Theory for Signal Processing in Psychoacoustics
This review chapter aims to strengthen the link between frame theory and
signal processing tasks in psychoacoustics. On the one side, the basic concepts
of frame theory are presented and some proofs are provided to explain those
concepts in some detail. The goal is to reveal to hearing scientists how this
mathematical theory could be relevant for their research. In particular, we
focus on frame theory in a filter bank approach, which is probably the most
relevant view-point for audio signal processing. On the other side, basic
psychoacoustic concepts are presented to stimulate mathematicians to apply
their knowledge in this field
Probabilistic frames: An overview
Finite frames can be viewed as mass points distributed in -dimensional
Euclidean space. As such they form a subclass of a larger and rich class of
probability measures that we call probabilistic frames. We derive the basic
properties of probabilistic frames, and we characterize one of their subclasses
in terms of minimizers of some appropriate potential function. In addition, we
survey a range of areas where probabilistic frames, albeit, under different
names, appear. These areas include directional statistics, the geometry of
convex bodies, and the theory of t-designs
Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by Fermi and Swift during the LIGO-Virgo Run O3b
We search for gravitational-wave signals associated with gamma-ray bursts (GRBs) detected by the Fermi and Swift satellites during the second half of the third observing run of Advanced LIGO and Advanced Virgo (2019 November 1 15:00 UTC-2020 March 27 17:00 UTC). We conduct two independent searches: A generic gravitational-wave transients search to analyze 86 GRBs and an analysis to target binary mergers with at least one neutron star as short GRB progenitors for 17 events. We find no significant evidence for gravitational-wave signals associated with any of these GRBs. A weighted binomial test of the combined results finds no evidence for subthreshold gravitational-wave signals associated with this GRB ensemble either. We use several source types and signal morphologies during the searches, resulting in lower bounds on the estimated distance to each GRB. Finally, we constrain the population of low-luminosity short GRBs using results from the first to the third observing runs of Advanced LIGO and Advanced Virgo. The resulting population is in accordance with the local binary neutron star merger rate. © 2022. The Author(s). Published by the American Astronomical Society
Narrowband Searches for Continuous and Long-duration Transient Gravitational Waves from Known Pulsars in the LIGO-Virgo Third Observing Run
Isolated neutron stars that are asymmetric with respect to their spin axis are possible sources of detectable continuous gravitational waves. This paper presents a fully coherent search for such signals from eighteen pulsars in data from LIGO and Virgo's third observing run (O3). For known pulsars, efficient and sensitive matched-filter searches can be carried out if one assumes the gravitational radiation is phase-locked to the electromagnetic emission. In the search presented here, we relax this assumption and allow both the frequency and the time derivative of the frequency of the gravitational waves to vary in a small range around those inferred from electromagnetic observations. We find no evidence for continuous gravitational waves, and set upper limits on the strain amplitude for each target. These limits are more constraining for seven of the targets than the spin-down limit defined by ascribing all rotational energy loss to gravitational radiation. In an additional search, we look in O3 data for long-duration (hours-months) transient gravitational waves in the aftermath of pulsar glitches for six targets with a total of nine glitches. We report two marginal outliers from this search, but find no clear evidence for such emission either. The resulting duration-dependent strain upper limits do not surpass indirect energy constraints for any of these targets. © 2022. The Author(s). Published by the American Astronomical Society
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