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About 3,658 papers for “Quantization (signal processing)”

Distributed average consensus with dithered quantization,” Signal Processing

Tuncer Can Aysal, Mark J. Coates, Michael G. Rabbat · 2008

Abstract—In this paper, we develop algorithms for distributed computation of averages of the node data over networks with band-width/power constraints or large volumes of data. Distributed averaging algorithms fail to achieve consensus when determin-istic uniform quantization is adopted. We propose a distributed algorithm in which the nodes utilize probabilistically quantized information, i.e., dithered quantization, to communicate with each other. The algorithm we develop is a dynamical system that gen-erates sequences achieving a consensus at one of the quantization values almost surely. In addition, we show that the expected value of the consensus is equal to the average of the original sensor data. We derive an upper bound on the mean-square-error per-formance of the probabilistically quantized distributed averaging (PQDA). Moreover, we show that the convergence of the PQDA is monotonic by studying the evolution of the minimum-length interval containing the node values. We reveal that the length of this interval is a monotonically nonincreasing function with limit zero. We also demonstrate that all the node values, in the worst case, converge to the final two quantization bins at the same rate as standard unquantized consensus. Finally, we report the results of simulations conducted to evaluate the behavior and the effectiveness of the proposed algorithm in various scenarios. Index Terms—Average consensus, distributed algorithms, dithering, probabilistic quantization, sensor networks. I.

Cited by 0

Quantization and Source Coding for Graph Signal Processing

Reingruber, Philipp · reposiTUm (TU Wien) · 2024

Die Graphsignalverarbeitung erlaubt, Daten auf unregelmäßigen Domänen – wie etwa auf Sensor- oder sozialen Netzwerken – darzustellen, anders als in der klassischen 1-D- oder 2-D-Signalverarbeitung. Die Frage der Quellkodierung von Graphsignalen auf diesen Domänen wurde jedoch bisher nicht ausreichend in der Literatur behandelt.In der vorliegenden Arbeit werden Transformationskodierungsverfahren für Graphsignale vorgestellt und diskutiert. Wir richten unser Augenmerk auf nichtstationäre Prozesse, welche wir durch Filterung und Modulation sowie durch bandförmige Frequenzkorrelationsmatrizen konstruieren. Die Kompressionsmethoden werden in Simulationen auf perturbierten zufälligen regulären Graphen, zufälligen geometrischen Graphen und Barabási-Albert-Graphen getestet. Unsere Simulationen zeigen, dass die Quantisierungsqualität von der Korrelation und dem Besetzungsgrad der Transformationskoeffizienten abhängt.Ein in der Literatur vorgeschlagenes Kompressionsverfahren stellt sich als numerisch instabil und rechenaufwändig heraus. Perfekte Dekorrelation mittels der Karhunen- Loève-Transformation ist ebenso mit großem Rechenaufwand verbunden. Daher stellen wir drei Kompressionsverfahren in drei unterschiedlichen Domänen vor. In der ersten Methode tasten wir im Knotenbereich ab und stellen das Signal mittels bandbeschränkter Rekonstruktion unter Verwendung der quantisierten Abtastwerte wieder her. Diese Methode liefert nur mit erheblicher Überabtastung bei schwacher Korrelation im Knotenbereich brauchbare Ergebnisse.Alternativ schlagen wir eine Kompression im Graphfrequenzbereich vor, da dies für die betrachteten nichtstationären Signalmodelle die robustesten Ergebnisse er- zielt. Trotz Korrelation bleibt die Kompressionsqualität annehmbar, da (insbesondere bandbeschränkte) Signale durch dünnbesetzte Koeffizientenvektoren dargestellt werden können. Beide Verfahren kommen der Rate-Distortion-Grenze nur in niederratigen Szenarien nahe. In vielen Fällen erhöhen Ausreißer die mittlere Verzerrung deutlich.Inspiriert von ihrem Pendant in der klassischen Signalverarbeitung führen wir die Graph-Gabor-Transformation (GGT) ein, eine abgetastete Version der gefensterten Graph-Fourier-Transformation (GFT). Das Abtastungsraster sollte an die Korrelation im Knoten- und Frequenzbereich angepasst sein, um schwächer korrelierte Transformationskoeffizienten zu erhalten. Unerwünschte Eigenschaften der GFT beeinträchtigen jedoch die Rasteranpassung. Darüber hinaus bilden weder die gefensterten GFT-Atome einen tight Frame, noch haben ihre Translations- und Modulationsoperatoren Gruppenstruktur. Dies beschränkt den Anwendungsbereich der GGT auf hochratige Kompressionsszenarien mit schwach korrelierten Prozessen auf Graphen mit niedriger Kohärenz.

Cited by 0Open access

Quantization in Compressive Sensing: A Signal Processing Approach

Isidora Stanković, Miloš Brajović, Miloš Daković et al. · IEEE Access · 2020

The influence of finite-length registers and the corresponding quantization effects on the reconstruction of sparse and approximately sparse signals from a reduced set of measurements is analyzed in this paper. For the nonquantized measurements, the compressive sensing (CS) framework provides highly accurate reconstruction algorithms that produce negligible errors when the reconstruction conditions are met. However, hardware implementations of signal processing algorithms inevitably involve finite-length registers and quantization of the measurements. A detailed analysis of the effects related to the measurement quantization, with an arbitrary number of bits, is provided in this paper. A unified novel mathematical model to characterize the influence of the quantization noise and the signal nonsparsity on the CS reconstruction is introduced. Using this model, an exact formula for the expected error energy in the CS-based reconstructed signal is derived, while in the literature its bounds have been reported only. The theory is validated through various numerical examples with quantized measurements, involving scenarios with approximately sparse signals, noise folding effect, and floating-point arithmetics.

Cited by 1Open access

Signal-dependent variable-resolution quantization for continuous-time digital signal processing

Mariya Kurchuk, Y. Tsividis · 2009

A variable-bit quantization scheme is proposed for use in the context of continuous-time digital signal processing, with resolution depended on signal speed. It is shown that a decrease in resolution for fast inputs does not corrupt the inband spectrum, while leading to power savings. Analysis and extensive simulations are provided.

Cited by 13

Multipurpose video signal processing unit

M.I. Minaev, N.S. Zimin, A.K. Zverev et al. · 2005

Two-channel radar signal processing PCI card with 100 MHz sampling frequency quantization is considered.

Cited by 0

Statistical Techniques for Signal Processing.

S. A. Kassam · 1983

Abstract : The area of nonlinear edge-preserving robust smoothing was one area of focus for our research. In this area a dissertation was completed. We have been able to give deterministic and statistical characterizations of the performance of some useful types of nonlinear filters which may be thought of as arising from the classical robust estimates of location (L- and M- estimates), and we have demonstrated their applicability in image processing. We are continuing to obtain new results in this area in our current work. In the area of nonparametric detection the case of narrowband signals in noise has been studied. We have established the natural counterparts of the sign-detection schemes for this class of signals. This material is currently being prepared for publication in a technical journal. A paper on quantization of data in narrowband signal detection was also published during the last grant year. On the subject of optimum quantization of data for signal detection (hypothesis testing) a comprehensive exposition has been written for publication as a chapter in a book to be published next year. These results on statistical optimization of quantization in detection systems are of considerable interest for digital implementations. Currently being revised for publication also is a paper on optimum quantization in matched filtering and smoothing of data. Finally, a paper on multi-input robust Wiener smoothing was also published during the last grant year.

Cited by 0

Statistical Techniques for Signal Processing

S.A. Kassam · 1981

Abstract : The area of nonlinear edge-preserving robust smoothing was one area of focus for our research. In this area a dissertation was completed. We have been able to give deterministic and statistical characterizations of the performance of some useful types of nonlinear filters which may be thought of as arising from the classical robust estimates of location (L- and M- estimates), and we have demonstrated their applicability in image processing. We are continuing to obtain new results in this area in our current work. In the area of nonparametric detection the case of narrowband signals in noise has been studied. We have established the natural counterparts of the sign-detection schemes for this class of signals. This material is currently being prepared for publication in a technical journal. A paper on quantization of data in narrowband signal detection was also published during the last grant year. On the subject of optimum quantization of data for signal detection (hypothesis testing) a comprehensive exposition has been written for publication as a chapter in a book to be published next year. These results on statistical optimization of quantization in detection systems are of considerable interest for digital implementations. Currently being revised for publication also is a paper on optimum quantization in matched filtering and smoothing of data. Finally, a paper on multi-input robust Wiener smoothing was also published during the last grant year.

Cited by 0

Signal quantization model for controlling power electronic circuits in digital signal processing

Wen Lu · Diagnostyka · 2026

This article discusses some key points of digital signal processing as it pertains to power electronics' digital control circuits.In this paper, we will go over some common issues with signal sampling, coherent sampling, sampling rate, jitter of the sampling pulse, successive vs. simultaneous collecting in a multichannel structure, resolution of the signal, interpolation while decimation, and digitization of analog circuits.But since they don't account for dynamic shifts and don't decrease interference, current signal estimate techniques can't provide reliable parameter data.In order to achieve high-precision signal parameter identification along with offering data for programs like wide-frequency fluctuation evaluation and enhancing energy efficiency issues, this work proposes a broadband indicate analysis approach that considers essential wave dynamics and reduces interference.To begin, knowledge about the waveforms and frequencies of the different components is extracted using the variational modal decomposition.Second, adjust the midrange frequencies so that they function as filters.Lastly, parameter estimation of wideband signals is accomplished using the least square approach.Noise, frequency dynamics modulation, frequency ramp changes, and other conditions are used to test the efficiency of the algorithm.The suggested approach successfully estimates the broadband signal's parameters with total vector errors of less than 3%, according to the results of the simulation.An improved method for determining the output signal-to-noise ratio in digital control circuits with three stages is detailed in this work.By taking these error sources into account and fixing them, we can reduce distortion and increase the signal-to-noise ratio, which improves the parameters of the output/input current and voltage and, in turn, the quality of the energy analyzing in power electronic devices.

Cited by 0Open access

Quantum Signal Processing -- . . .

Yonina C. Eldar, et al. · 2008

In this article we present a signal processing framework that we refer to as quantum signal processing (QSP) [1] that is aimed at developing new or modifying existing signal processing algorithms by borrowing from the principles of quantum mechanics and some of its interesting axioms and constraints. However, in contrast to such fields as quantum computing and quantum information theory, it does not inherently depend on the physics associated with quantum mechanics. Consequently, in developing the QSP framework we are free to Measurement, Quantization, Consistency This famous strobe photograph taken by Dr. Harold “Doc ” Edgerton at MIT in 1957 captures the transition of a milk drop as it splashes from a single drop into a continuous ring and then coalesces into droplets forming the points of a coronet. Copyright Harold and Ester Edgerton Family Foundation. Reproduced with permission.

Cited by 0

Signal processing, image processing, and pattern recognition

Choice Reviews Online · 1992

A detailed exposition of the main areas of signal processing, this book is divided into three sections: one-dimensional signal processing and digital filters; two-dimensional signal processing and image processing; and pattern recognition. Among the more specific topics covered are: analog filters; discrete systems and signals; non-recursive filters; FFT; IIR design; quantization effects; and hardware and software design. There is also material on system stability, picture enhancement and restoration, and parallel processing methods, as well as a comprehensive treatment of syntactic methods, parsing and neural networks.

Cited by 103

Modern Digital Signal Processing

R. Cristi · Medical Entomology and Zoology · 2003

1. FUNDAMENTALS OF SIGNALS AND SYSTEMS. Signals. Systems. Fourier Analysis of Discrete Time Signals. Fourier Analysis of Continuous Time Signals. 2. DISCRETE TIME PROCESSING OF CONTINUOUS TIME SIGNALS. Introduction. Structure of a Digital Filter. Frequency Domain Analysis of a Digital Filter. Quantization Errors. Prediction-Based Sampling Methods: Sigma and Sigma-Delta Modulation. 3. FOURIER ANALYSIS OF DISCRETE TIME SIGNALS. Introduction. Discrete Time Fourier Transform (DTFT). Discrete Fourier Transform (DFT). The DFT as an Estimate of the DTFT. DFT for Spectral Estimation. DFT for Convolution. DFT/DCT for Compression. The Fast Fourier Transform (FFT). 4. DIGITAL FILTERS. Introduction. Ideal Versus Nonideal Filters. Finite Impulse Response (FIR) Filters. Infinite Impulse Response (IIR) Filters. 5. DIGITAL FILTERS IMPLEMENTATION. Introduction. Elementary Operations. State Space Realization of Digital Filters. Robust Implementation of Digital Filters. Robust Implementation of Equiripple FIR Filters. 6. MULTIRATE DIGITAL SIGNAL PROCESSING: FUNDAMENTALS. Introduction. Statement of the Problem and Definitions. Analysis of Downsampling and Upsampling. Sampling Rate Conversion by a Rational Factor. Multistage Implementation of Digital Filters. Efficient Implementation of Multirate Systems. Application of Multirate DSP: Digital-to-Analog Conversion. Sampling Frequency and Quantization Error. 7. DFT FILTER BANKS AND TRANSMULTIPLEXERS. Introduction. DFT Filter Banks. Maximally Decimated DFT Filter Banks and Transmultiplexers. Transmultiplexers. Application of Transmultiplexers to Digital Communication Modulation. 8. MAXIMALLY DECIMATED FILTER BANKS. Introduction. Vector Spaces. Two-Channel Perfect Reconstruction Conditions. Design of Perfect Reconstruction Filter Banks with Real Coefficients. Lattice Implementation of Orthonormal Filter Banks. Application to an Audio Signal. 9. TIME FREQUENCY EXPANSION: AN INTRODUCTION. Introduction. The Short Time Fourier Transform (STFT). The Gabor Transform (GT). The Wavelet Transform. Recursive Multiresolution Decomposition. APPENDIXES. INDEX.

Cited by 131

Digital Signal Processing

Steiglitz, Ken, Liu, Bede · Defense Technical Information Center (DTIC) · 1992

A wide variety of problems in digital signal processing were studied, with emphasis on the scalability of architectures for large array processors, timing and reliability limits in large arrays, delay performance of statistical multiplexers, robust signal processing, and digital image coding and processing. Results in the study of array processors include the development of a particular architecture that scales very well for iterative computations on a regular lattice, and a testing method particularly suited to lattice-gas computations. Related work describes design methods for redundant arrays, and arrays that incorporate error detection and correction. In the study of the delay performance of statistical multiplexers, a method is given for computation of the queue-length probability distribution function in the presence of voice traffic. The work in robust signal processing studies the effect of incomplete information on the performance of matched filters. An approach is presented for the compression of color images with limited palette size that does not require color quantization of the decoded image. For comparable quality and bit rates, the proposed technique significantly reduces the decoder computational complexity. Finally, different approaches are compared for block motion compensation coding of interlaced sequences. It is shown that proper use of that redundancy can significantly improve the coding efficiency.

Cited by 0

Digital Signal Processing 13 (2003) 172--197

Www Elsevier Com, Ro Farias Estrozi, A Luiz Gonzaga Rios-filho et al. · 2008

A careful comparison of three numeric techniques for estimation of the curvature along spatially quantized contours is reported. Two of the considered techniques are based on the Fourier transform (operating over 1D and 2D signals) and Gaussian regularization required to attenuate the spatial quantization noise. While the 1D approach has been reported before and used in a series of applications, the 2D Fourier transform-based method is reported in this article for the first time. The third approach, based on splines, represents a more traditional alternative. Three classes of parametric curves are investigated: analytical, B-splines, and synthesized in the Fourier domain. Four quantization schemes are considered: grid intersect quantization, square box quantization, a table scanner, and a video camera. The performances of the methods are evaluated in terms of their execution speed, curvature error, and sensitivity to the involved parameters. The third approach resulted the fastest, but implied larger errors; the Fourier methods allowed higher accuracy and were robust to parameter configurations. The 2D Fourier method provides the curvature values along the whole image, but exhibits interference in some situations. Such results are important not only for characterizing the relative performance of the considered methods, but also for providing practical guidelines for those interested in applying those techniques to real problems.

Cited by 0

Literature Survey EE 381K Multi-Dimensional Signal Processing

James Fung · 2008

The effect of steering delay quantization on beamformer frequency and azimuth response is not well understood. This project will attempt to analyze the relationship between steering delay quantization, with its corresponding impact on computational complexity, and beamformer response error. Results found here should benefit both conventional beamforming and modern adaptive beamforming applications. I.

Cited by 0

Mixed-Domain Signal Processing

Y. Tsividis · 2006

We argue that mixing domains within circuits and systems can result in new possibilities. We have presented several examples of mixed-domain systems. Internally time-varying (but externally time-invariant) circuits can be designed to consume only the minimum power needed for each task at hand. Several techniques have been presented for making this possible, while avoiding output transients. Internally nonlinear (but externally linear) digital filters make possible 1) keeping internal signal strength large, even for small-strength inputs and 2) maximizing signal-to-error ratio for a large range of input signals. Continuous-time DSP may offer certain advantages of digital technology without its drawbacks: 1) fully digital (noise immunity, programmability), 2) no sampling; thus no signal aliasing, 3) smaller in-band quantization error, and 4) power goes down with decreasing input activity. All of the principles discussed are at the early research stage; none has reached commercial feasibility. Thorough experimental validation and application of some of the principles presented are being pursued

Cited by 0

Optimal vector quantization: from signal processing to clustering and numerical probability

Pagès, Gilles · Centre International de Rencontres Mathématiques · 2017

Optimal vector quantization has been originally introduced in Signal processing as a discretization method of random signals, leading to an optimal trade-off between the speed of transmission and the quality of the transmitted signal. In machine learning, similar methods applied to a dataset are the historical core of unsupervised classification methods known as “clustering”. In both case it appears as an optimal way to produce a set of weighted prototypes (or codebook) which makes up a kind of skeleton of a dataset, a signal and more generally, from a mathematical point of view, of a probability distribution. Quantization has encountered in recent years a renewed interest in various application fields like automatic classification, learning algorithms, optimal stopping and stochastic control, Backward SDEs and more generally numerical probability. In all these various applications, practical implementation of such clustering/quantization methods more or less rely on two procedures (and their countless variants): the Competitive Learning Vector Quantization $(CLV Q)$ which appears as a stochastic gradient descent derived from the so-called distortion potential and the (randomized) Lloyd's procedure (also known as k- means algorithm, nu ees dynamiques) which is but a fixed point search procedure. Batch version of those procedures can also be implemented when dealing with a dataset (or more generally a discrete distribution). In a more formal form, if is probability distribution on an Euclidean space $\mathbb{R}^d$, the optimal quantization problem at level $N$ boils down to exhibiting an $N$-tuple $(x_{1}^{²}, . . . , x_{N}^{²})$, solution to argmin$_{(x1,\dotsb,x_N)\epsilon(\mathbb{R}^d)^N} \int_{\mathbb{R}^d 1\le i\le N} \min |x_i-\xi|^2 \mu(d\xi)$ and its distribution i.e. the weights $(\mu(C(x_{i}^{²}))_{1\le i\le N}$ where $(C(x_{i}^{²})$ is a (Borel) partition of $\mathbb{R}^d$ satisfying $C(x_{i}^{²})\subset \lbrace\xi\epsilon\mathbb{R}^d :|x_{i}^{²} -\xi|\le_{1\le j\le N} \min |x_{j}^{²}-\xi|\rbrace$. To produce an unsupervised classification (or clustering) of a (large) dataset $(\xi_k)_{1\le k\le n}$, one considers its empirical measure $\mu=\frac{1}{n}\sum_{k=1}^{n}\delta_{\xi k}$ whereas in numerical probability $\mu = \mathcal{L}(X)$ where $X$ is an $\mathbb{R}^d$-valued simulatable random vector. In both situations, $CLV Q$ and Lloyd's procedures rely on massive sampling of the distribution $\mu$. As for clustering, the classification into $N$ clusters is produced by the partition of the dataset induced by the Voronoi cells $C(x_{i}^{²}), i = 1, \dotsb, N$ of the optimal quantizer. In this second case, which is of interest for solving non linear problems like Optimal stopping problems (variational inequalities in terms of PDEs) or Stochastic control problems (HJB equations) in medium dimensions, the idea is to produce a quantization tree optimally fitting the dynamics of (a time discretization) of the underlying structure process. We will explore (briefly) this vast panorama with a focus on the algorithmic aspects where few theoretical results coexist with many heuristics in a burgeoning literature. We will present few simulations in two dimensions.

Cited by 0Open access