16,718 research outputs found
Sampling and Exact Reconstruction of Pulses with Variable Width
Recent sampling results enable the reconstruction of signals composed of streams of fixed-shaped pulses. These results have found applications in topics as varied as channel estimation, biomedical imaging and radio astronomy. However, in many real signals, the pulse shapes vary throughout the signal. In this paper, we show how to sample and perfectly reconstruct Lorentzian pulses with variable width. Since a stream of Lorentzian pulses has a finite number of degrees of freedom per unit time, it belongs to the class of signals with finite rate of innovation (FRI). In the noiseless case, perfect recovery is guaranteed by a set of theorems. In addition, we verify that our algorithm is robust to model-mismatch and noise. This allows us to apply the technique to two practical applications: electrocardiogram (ECG) compression and bidirectional reflectance distribution function (BRDF) sampling. ECG signals are one dimensional, but the BRDF is a higher dimensional signal, which is more naturally expressed in a spherical coordinate system; this motivated us to extend the theory to the 2D and spherical cases. Experiments on real data demonstrate the viability of the proposed model for ECG acquisition and compression, as well as the efficient representation and low-rate sampling of specular BRDFs
A Bayesian method for pulsar template generation
Extracting Times of Arrival from pulsar radio signals depends on the
knowledge of the pulsars pulse profile and how this template is generated. We
examine pulsar template generation with Bayesian methods. We will contrast the
classical generation mechanism of averaging intensity profiles with a new
approach based on Bayesian inference. We introduce the Bayesian measurement
model imposed and derive the algorithm to reconstruct a "statistical template"
out of noisy data. The properties of these "statistical templates" are analysed
with simulated and real measurement data from PSR B1133+16. We explain how to
put this new form of template to use in analysing secondary parameters of
interest and give various examples: We implement a nonlinear filter for
determining ToAs of pulsars. Applying this method to data from PSR J1713+0747
we derive ToAs self consistently, meaning all epochs were timed and we used the
same epochs for template generation. While the average template contains
fluctuations and noise as unavoidable artifacts, we find that the "statistical
template" derived by Bayesian inference quantifies fluctuations and remaining
uncertainty. This is why the algorithm suggested turns out to reconstruct
templates of statistical significance from ten to fifty single pulses. A moving
data window of fifty pulses, taking out one single pulse at the beginning and
adding one at the end of the window unravels the characteristics of the methods
to be compared. It shows that the change induced in the classical
reconstruction is dominated by random fluctuations for the average template,
while statistically significant changes drive the dynamics of the proposed
method's reconstruction. The analysis of phase shifts with simulated data
reveals that the proposed nonlinear algorithm is able to reconstruct correct
phase information along with an acceptable estimation of the remaining
uncertainty.Comment: 21 pages, 16 figures, submitted to MNRA
Calculation of time resolution of the J-PET tomograph using the Kernel Density Estimation
In this paper we estimate the time resolution of the J-PET scanner built from
plastic scintillators. We incorporate the method of signal processing using the
Tikhonov regularization framework and the Kernel Density Estimation method. We
obtain simple, closed-form analytical formulas for time resolutions. The
proposed method is validated using signals registered by means of the single
detection unit of the J-PET tomograph built out from 30 cm long plastic
scintillator strip. It is shown that the experimental and theoretical results,
obtained for the J-PET scanner equipped with vacuum tube photomultipliers, are
consistent.Comment: 25 pages, 11 figure
Common pulse retrieval algorithm: a fast and universal method to retrieve ultrashort pulses
We present a common pulse retrieval algorithm (COPRA) that can be used for a
broad category of ultrashort laser pulse measurement schemes including
frequency-resolved optical gating (FROG), interferometric FROG, dispersion
scan, time domain ptychography, and pulse shaper assisted techniques such as
multiphoton intrapulse interference phase scan (MIIPS). We demonstrate its
properties in comprehensive numerical tests and show that it is fast, reliable
and accurate in the presence of Gaussian noise. For FROG it outperforms
retrieval algorithms based on generalized projections and ptychography.
Furthermore, we discuss the pulse retrieval problem as a nonlinear
least-squares problem and demonstrate the importance of obtaining a
least-squares solution for noisy data. These results improve and extend the
possibilities of numerical pulse retrieval. COPRA is faster and provides more
accurate results in comparison to existing retrieval algorithms. Furthermore,
it enables full pulse retrieval from measurements for which no retrieval
algorithm was known before, e.g., MIIPS measurements
Temporal solitons in optical microresonators
Dissipative solitons can emerge in a wide variety of dissipative nonlinear
systems throughout the fields of optics, medicine or biology. Dissipative
solitons can also exist in Kerr-nonlinear optical resonators and rely on the
double balance between parametric gain and resonator loss on the one hand and
nonlinearity and diffraction or dispersion on the other hand. Mathematically
these solitons are solution to the Lugiato-Lefever equation and exist on top of
a continuous wave (cw) background. Here we report the observation of temporal
dissipative solitons in a high-Q optical microresonator. The solitons are
spontaneously generated when the pump laser is tuned through the effective zero
detuning point of a high-Q resonance, leading to an effective red-detuned
pumping. Red-detuned pumping marks a fundamentally new operating regime in
nonlinear microresonators. While usually unstablethis regime acquires unique
stability in the presence of solitons without any active feedback on the
system. The number of solitons in the resonator can be controlled via the pump
laser detuning and transitions to and between soliton states are associated
with discontinuous steps in the resonator transmission. Beyond enabling to
study soliton physics such as soliton crystals our observations open the route
towards compact, high repetition-rate femto-second sources, where the operating
wavelength is not bound to the availability of broadband laser gain media. The
single soliton states correspond in the frequency domain to low-noise optical
frequency combs with smooth spectral envelopes, critical to applications in
broadband spectroscopy, telecommunications, astronomy and low phase-noise
microwave generation.Comment: Includes Supplementary Informatio
Non-invasive, near-field terahertz imaging of hidden objects using a single pixel detector
Terahertz (THz) imaging has the ability to see through otherwise opaque
materials. However, due to the long wavelengths of THz radiation
({\lambda}=300{\mu}m at 1THz), far-field THz imaging techniques are heavily
outperformed by optical imaging in regards to the obtained resolution. In this
work we demonstrate near-field THz imaging with a single-pixel detector. We
project a time-varying optical mask onto a silicon wafer which is used to
spatially modulate a pulse of THz radiation. The far-field transmission
corresponding to each mask is recorded by a single element detector and this
data is used to reconstruct the image of an object placed on the far side of
the silicon wafer. We demonstrate a proof of principal application where we
image a printed circuit board on the underside of a 115{\mu}m thick silicon
wafer with ~100{\mu}m ({\lambda}/4) resolution. With subwavelength resolution
and the inherent sensitivity to local conductivity provided by the THz probe
frequencies, we show that it is possible to detect fissures in the circuitry
wiring of a few microns in size. Imaging systems of this type could have other
uses where non-invasive measurement or imaging of concealed structures with
high resolution is necessary, such as in semiconductor manufacturing or in
bio-imaging
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