1,631 research outputs found
Sampling and Super-resolution of Sparse Signals Beyond the Fourier Domain
Recovering a sparse signal from its low-pass projections in the Fourier
domain is a problem of broad interest in science and engineering and is
commonly referred to as super-resolution. In many cases, however, Fourier
domain may not be the natural choice. For example, in holography, low-pass
projections of sparse signals are obtained in the Fresnel domain. Similarly,
time-varying system identification relies on low-pass projections on the space
of linear frequency modulated signals. In this paper, we study the recovery of
sparse signals from low-pass projections in the Special Affine Fourier
Transform domain (SAFT). The SAFT parametrically generalizes a number of well
known unitary transformations that are used in signal processing and optics. In
analogy to the Shannon's sampling framework, we specify sampling theorems for
recovery of sparse signals considering three specific cases: (1) sampling with
arbitrary, bandlimited kernels, (2) sampling with smooth, time-limited kernels
and, (3) recovery from Gabor transform measurements linked with the SAFT
domain. Our work offers a unifying perspective on the sparse sampling problem
which is compatible with the Fourier, Fresnel and Fractional Fourier domain
based results. In deriving our results, we introduce the SAFT series (analogous
to the Fourier series) and the short time SAFT, and study convolution theorems
that establish a convolution--multiplication property in the SAFT domain.Comment: 42 pages, 3 figures, manuscript under revie
Enhanced monopulse radar tracking using optimum fractional Fourier transform
Conventional monopulse radar processors are used to track a target that appears in the look direction beam width. The distortion produced when additional targets appear in the look direction beam width can cause severe erroneous outcomes from the monopulse processor. This leads to errors in the target tracking angles that may cause target mistracking. A new signal processing algorithm is presented in this paper which offers a solution to this problem. The technique is based on the use of optimal Fractional Fourier Transform (FrFT) filtering. The relative performance of the new filtering method over traditional based methods is assessed using standard deviation angle estimation error (STDAE) for a range of simulated environments. The proposed system configuration succeeds in significantly cancelling additional target signals appearing in the look direction beam width even if these targets have the same Doppler frequency
Super-Resolution in Phase Space
This work considers the problem of super-resolution. The goal is to resolve a
Dirac distribution from knowledge of its discrete, low-pass, Fourier
measurements. Classically, such problems have been dealt with parameter
estimation methods. Recently, it has been shown that convex-optimization based
formulations facilitate a continuous time solution to the super-resolution
problem. Here we treat super-resolution from low-pass measurements in Phase
Space. The Phase Space transformation parametrically generalizes a number of
well known unitary mappings such as the Fractional Fourier, Fresnel, Laplace
and Fourier transforms. Consequently, our work provides a general super-
resolution strategy which is backward compatible with the usual Fourier domain
result. We consider low-pass measurements of Dirac distributions in Phase Space
and show that the super-resolution problem can be cast as Total Variation
minimization. Remarkably, even though are setting is quite general, the bounds
on the minimum separation distance of Dirac distributions is comparable to
existing methods.Comment: 10 Pages, short paper in part accepted to ICASSP 201
A new fractional Fourier transform based monopulse tracking radar processor
Conventional monopulse radar processors are used to track a target that appears in the look direction beam width. The distortion produced when additional targets appear in the look direction beam width can cause severe erroneous outcomes from the monopulse processor. This leads to errors in the target tracking angles that may cause the target tracker to fail. A new signal processing algorithm is presented in this paper that is based on the use of optimal Fractional Fourier Transform (FrFT) filtering to solve this problem. The relative performance of the new filtering method over traditional based methods is assessed using standard deviation angle estimation error (STDAE) for a range of simulated environments. The proposed system configurations with the optimum FrFT filters succeeds in effectively cancelling additional target signals appearing in the look direction beam width
A Mock Data Challenge for the Einstein Gravitational-Wave Telescope
Einstein Telescope (ET) is conceived to be a third generation
gravitational-wave observatory. Its amplitude sensitivity would be a factor ten
better than advanced LIGO and Virgo and it could also extend the low-frequency
sensitivity down to 1--3 Hz, compared to the 10--20 Hz of advanced detectors.
Such an observatory will have the potential to observe a variety of different
GW sources, including compact binary systems at cosmological distances. ET's
expected reach for binary neutron star (BNS) coalescences is out to redshift
and the rate of detectable BNS coalescences could be as high as one
every few tens or hundreds of seconds, each lasting up to several days. %in the
sensitive frequency band of ET. With such a signal-rich environment, a key
question in data analysis is whether overlapping signals can be discriminated.
In this paper we simulate the GW signals from a cosmological population of BNS
and ask the following questions: Does this population create a confusion
background that limits ET's ability to detect foreground sources? How efficient
are current algorithms in discriminating overlapping BNS signals? Is it
possible to discern the presence of a population of signals in the data by
cross-correlating data from different detectors in the ET observatory? We find
that algorithms currently used to analyze LIGO and Virgo data are already
powerful enough to detect the sources expected in ET, but new algorithms are
required to fully exploit ET data.Comment: accepted for publication in Physical Review D -- 18 pages, 8 figure
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