11,089 research outputs found
Estimation from quantized Gaussian measurements: when and how to use dither
Subtractive dither is a powerful method for removing the signal dependence of quantization noise for coarsely quantized signals. However, estimation from dithered measurements often naively applies the sample mean or midrange, even when the total noise is not well described with a Gaussian or uniform distribution. We show that the generalized Gaussian distribution approximately describes subtractively dithered, quantized samples of a Gaussian signal. Furthermore, a generalized Gaussian fit leads to simple estimators based on order statistics that match the performance of more complicated maximum likelihood estimators requiring iterative solvers. The order statistics-based estimators outperform both the sample mean and midrange for nontrivial sums of Gaussian and uniform noise. Additional analysis of the generalized Gaussian approximation yields rules of thumb for determining when and how to apply dither to quantized measurements. Specifically, we find subtractive dither to be beneficial when the ratio between the Gaussian standard deviation and quantization interval length is roughly less than one-third. When that ratio is also greater than 0.822/K^0.930 for the number of measurements K > 20, estimators we present are more efficient than the midrange.https://arxiv.org/abs/1811.06856Accepted manuscrip
ITOS VHRR on-board data compression study
Data compression methods for ITOS VHRR data were studied for a tape recorder record-and playback application. A playback period of 9 minutes was assumed with a nominal 18 minute record period for a 2-to-1 compression ratio. Both analog and digital methods were considered with the conclusion that digital methods should be used. Two system designs were prepared. One is a PCM system and the other is an entropy-coded predictive-quantization, sometimes called entropy-coded DPCM or just DPCM, system. Both systems use data management principles to transmit only the necessary data. Both systems use a medium capacity standard tape recorder from specifications provided by the technical officer. The 10 to the 9th power bit capacity of the recorder is the basic limitation on the compression ratio. Both systems achieve the minimum desired 2 to 1 compression ratio. A slower playback rate can be used with the DPCM system due to a higher compression factor for better link performance at a given CNR in terms of bandwidth utilization and error rate. The report is divided into two parts. The first part summarizes the theoretical conclusions of the second part and presents the system diagrams. The second part is a detailed analysis based upon an empirically derived random process model arrived at from specifications and measured data provided by the technical officer
Quadratic optimal functional quantization of stochastic processes and numerical applications
In this paper, we present an overview of the recent developments of
functional quantization of stochastic processes, with an emphasis on the
quadratic case. Functional quantization is a way to approximate a process,
viewed as a Hilbert-valued random variable, using a nearest neighbour
projection on a finite codebook. A special emphasis is made on the
computational aspects and the numerical applications, in particular the pricing
of some path-dependent European options.Comment: 41 page
Approximate Kalman-Bucy filter for continuous-time semi-Markov jump linear systems
The aim of this paper is to propose a new numerical approximation of the
Kalman-Bucy filter for semi-Markov jump linear systems. This approximation is
based on the selection of typical trajectories of the driving semi-Markov chain
of the process by using an optimal quantization technique. The main advantage
of this approach is that it makes pre-computations possible. We derive a
Lipschitz property for the solution of the Riccati equation and a general
result on the convergence of perturbed solutions of semi-Markov switching
Riccati equations when the perturbation comes from the driving semi-Markov
chain. Based on these results, we prove the convergence of our approximation
scheme in a general infinite countable state space framework and derive an
error bound in terms of the quantization error and time discretization step. We
employ the proposed filter in a magnetic levitation example with markovian
failures and compare its performance with both the Kalman-Bucy filter and the
Markovian linear minimum mean squares estimator
Elliptic Quantum Billiard
The exact and semiclassical quantum mechanics of the elliptic billiard is
investigated. The classical system is integrable and exhibits a separatrix,
dividing the phasespace into regions of oscillatory and rotational motion. The
classical separability carries over to quantum mechanics, and the Schr\"odinger
equation is shown to be equivalent to the spheroidal wave equation. The quantum
eigenvalues show a clear pattern when transformed into the classical action
space. The implication of the separatrix on the wave functions is illustrated.
A uniform WKB quantization taking into account complex orbits is shown to be
adequate for the semiclassical quantization in the presence of a separatrix.
The pattern of states in classical action space is nicely explained by this
quantization procedure. We extract an effective Maslov phase varying smoothly
on the energy surface, which is used to modify the Berry-Tabor trace formula,
resulting in a summation over non-periodic orbits. This modified trace formula
produces the correct number of states, even close to the separatrix. The
Fourier transform of the density of states is explained in terms of classical
orbits, and the amplitude and form of the different kinds of peaks is
analytically calculated.Comment: 33 pages, Latex2e, 19 figures,macros: epsfig, amssymb, amstext,
submitted to Annals of Physic
Multiple-Description Coding by Dithered Delta-Sigma Quantization
We address the connection between the multiple-description (MD) problem and
Delta-Sigma quantization. The inherent redundancy due to oversampling in
Delta-Sigma quantization, and the simple linear-additive noise model resulting
from dithered lattice quantization, allow us to construct a symmetric and
time-invariant MD coding scheme. We show that the use of a noise shaping filter
makes it possible to trade off central distortion for side distortion.
Asymptotically as the dimension of the lattice vector quantizer and order of
the noise shaping filter approach infinity, the entropy rate of the dithered
Delta-Sigma quantization scheme approaches the symmetric two-channel MD
rate-distortion function for a memoryless Gaussian source and MSE fidelity
criterion, at any side-to-central distortion ratio and any resolution. In the
optimal scheme, the infinite-order noise shaping filter must be minimum phase
and have a piece-wise flat power spectrum with a single jump discontinuity. An
important advantage of the proposed design is that it is symmetric in rate and
distortion by construction, so the coding rates of the descriptions are
identical and there is therefore no need for source splitting.Comment: Revised, restructured, significantly shortened and minor typos has
been fixed. Accepted for publication in the IEEE Transactions on Information
Theor
Adaptive Quantizers for Estimation
In this paper, adaptive estimation based on noisy quantized observations is
studied. A low complexity adaptive algorithm using a quantizer with adjustable
input gain and offset is presented. Three possible scalar models for the
parameter to be estimated are considered: constant, Wiener process and Wiener
process with deterministic drift. After showing that the algorithm is
asymptotically unbiased for estimating a constant, it is shown, in the three
cases, that the asymptotic mean squared error depends on the Fisher information
for the quantized measurements. It is also shown that the loss of performance
due to quantization depends approximately on the ratio of the Fisher
information for quantized and continuous measurements. At the end of the paper
the theoretical results are validated through simulation under two different
classes of noise, generalized Gaussian noise and Student's-t noise
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