Search results for "signal processing"

showing 10 items of 2451 documents

On the loopless generation of binary tree sequences

1998

Weight sequences were introduced by Pallo in 1986 for coding binary trees and he presented a constant amortized time algorithm for their generation in lexicographic order. A year later, Roelants van Baronaigien and Ruskey developed a recursive constant amortized time algorithm for generating Gray code for binary trees in Pallo's representation. It is common practice to find a loopless generating algorithm for a combinatorial object when enunciating a Gray code for this object. In this paper we regard weight sequences as variations and apply a Williamson algorithm in order to obtain a loopless generating algorithm for the Roelants van Baronaigien and Ruskey's Gray code for weight sequences.

Discrete mathematicsAmortized analysisBinary treeLexicographical orderPseudorandom binary sequenceComputer Science ApplicationsTheoretical Computer ScienceGray codeCombinatoricsSignal ProcessingBinary codeInformation SystemsCoding (social sciences)MathematicsInformation Processing Letters
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Analysis of Optimal High Resolution and Fixed Rate Scalar Quantization

2009

In 2001, Hui and Neuhoff proposed a uniform quantizer with overload for the quantization of scalar signals and derived the asymptotically optimal size of the quantization bins in the high-bitrate limit. The purpose of the present paper is to prove a quantitatively more precise version of this result which, at the same time, is valid for a more general, quite natural class of probability distributions that requires only little regularity and includes, for instance, positive Lipschitz-continuous functions of unit integral.

Discrete mathematicsAsymptotically optimal algorithmScalar quantizationQuantization (signal processing)Applied mathematicsHigh resolutionProbability distributionLibrary and Information SciencesInformation theoryNatural classComputer Science ApplicationsInformation SystemsMathematicsIEEE Transactions on Information Theory
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Root-restricted Kleenean rotations

2010

We generalize the Kleene theorem to the case where nonassociative products are used. For this purpose, we apply rotations restricted to the root of binary trees.

Discrete mathematicsBinary treeMathematics::Rings and AlgebrasRoot (chord)Kleene theoremComputer Science ApplicationsTheoretical Computer ScienceCombinatoricsMathematics::Group TheoryProduct (mathematics)Signal ProcessingRotation (mathematics)Computer Science::Formal Languages and Automata TheoryInformation SystemsMathematicsInformation Processing Letters
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Generating binary trees by Glivenko classes on Tamari lattices

2003

Using algebraic-theoretic results, we give an algorithm for generating binary trees within Glivenko classes in Tamari lattices. Tamari lattices are lattices of binary trees endowed by the well-known rotation transformation.

Discrete mathematicsMathematics::CombinatoricsBinary treeHigh Energy Physics::LatticeGraph theoryComputer Science ApplicationsTheoretical Computer ScienceCombinatoricsLattice (order)Signal ProcessingTamari latticeRotation (mathematics)Information SystemsMathematicsInformation Processing Letters
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Tensor product multiresolution analysis with error control for compact image representation

2002

A class of multiresolution representations based on nonlinear prediction is studied in the multivariate context based on tensor product strategies. In contrast to standard linear wavelet transforms, these representations cannot be thought of as a change of basis, and the error induced by thresholding or quantizing the coefficients requires a different analysis. We propose specific error control algorithms which ensure a prescribed accuracy in various norms when performing such operations on the coefficients. These algorithms are compared with standard thresholding, for synthetic and real images.

Discrete mathematicsMultiresolution analysisMathematicsofComputing_NUMERICALANALYSISWavelet transformImage processingReal imageThresholdingTensor productControl and Systems EngineeringSignal ProcessingComputer Vision and Pattern RecognitionElectrical and Electronic EngineeringChange of basisAlgorithmSoftwareMathematicsImage compressionSignal Processing
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Loop-free Gray code algorithm for the e-restricted growth functions

2011

The subject of Gray codes algorithms for the set partitions of {1,2,...,n} had been covered in several works. The first Gray code for that set was introduced by Knuth (1975) [5], later, Ruskey presented a modified version of [email protected]?s algorithm with distance two, Ehrlich (1973) [3] introduced a loop-free algorithm for the set of partitions of {1,2,...,n}, Ruskey and Savage (1994) [9] generalized [email protected]?s results and give two Gray codes for the set of partitions of {1,2,...,n}, and recently, Mansour et al. (2008) [7] gave another Gray code and loop-free generating algorithm for that set by adopting plane tree techniques. In this paper, we introduce the set of e-restricte…

Discrete mathematicsPrefix codeGeneralizationOrder (ring theory)Computer Science ApplicationsTheoretical Computer ScienceCombinatoricsSet (abstract data type)Gray codeTree (descriptive set theory)Signal ProcessingFunction representationRepresentation (mathematics)AlgorithmInformation SystemsMathematicsInformation Processing Letters
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Exceptional Quantum Walk Search on the Cycle

2016

Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips, staying in a uniform probability distribution for all time. We prove that the one-dimensional periodic lattice or cycle with any arrangement of marked vertices is such an exceptional configuration. Using this discovery, we construct a search problem where the quantum walk's random sampling yields an arbitrary speedup in query complexity over the classical random walk's hitting time. In this context, however, the mixing time to prepare the initial uniform state…

Discrete mathematicsQuantum PhysicsSpeedupHitting timeFOS: Physical sciencesStatistical and Nonlinear PhysicsContext (language use)Random walk01 natural sciences010305 fluids & plasmasTheoretical Computer ScienceElectronic Optical and Magnetic MaterialsQuadratic equationModeling and Simulation0103 physical sciencesSignal ProcessingSearch problemQuantum walkElectrical and Electronic Engineering010306 general physicsQuantum Physics (quant-ph)MathematicsSign (mathematics)
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A general metric regularity in asplund banach spaces

1998

This paper establishes a simple and easily-applied criterion for determining whether a multivalued mapping is metrically regular relatively to a subset in the range space.

Discrete mathematicsRange (mathematics)Control and OptimizationSimple (abstract algebra)Signal ProcessingMetric (mathematics)Banach spaceSpace (mathematics)AnalysisComputer Science ApplicationsMathematicsNumerical Functional Analysis and Optimization
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Introduction: Periodic Signals and Filters

2018

In this chapter we briefly outline some well-known facts about Discrete-time periodic signals, their transforms and periodic digital filters and filter banks. For details we refer to the classical textbook A. V. Oppenheim and R. W. Schafer (Discrete-Time Signal Processing, Prentice Hall, New York, 2010, [3]) and Volume I of our book (Averbuch, Neittaanmaki and Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Periodic Splines, vol. 1 (Springer, Berlin, 2014)) [1] Throughout the volume, unless other indicated, \(N=2^{j}, \;j\in \mathbb {N}\).

Discrete mathematicsSpline (mathematics)Signal processingSpline waveletImage processingDigital filterMathematics
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Online Scheduling of Task Graphs on Heterogeneous Platforms

2020

Modern computing platforms commonly include accelerators. We target the problem of scheduling applications modeled as task graphs on hybrid platforms made of two types of resources, such as CPUs and GPUs. We consider that task graphs are uncovered dynamically, and that the scheduler has information only on the available tasks, i.e., tasks whose predecessors have all been completed. Each task can be processed by either a CPU or a GPU, and the corresponding processing times are known. Our study extends a previous $4\sqrt{m/k}$ 4 m / k -competitive online algorithm by Amaris et al. [1] , where $m$ m is the number of CPUs and $k$ k the number of GPUs ( $m\geq k$ m ≥ k ). We prove that no online…

Discrete mathematics[INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC]020203 distributed computingScheduleCompetitive analysisComputer scienceHeuristicSchedulingOnline algorithmsProcessor schedulingSymmetric multiprocessor system02 engineering and technologyUpper and lower boundsGraphScheduling (computing)Computational Theory and MathematicsHardware and ArchitectureSignal Processing0202 electrical engineering electronic engineering information engineeringTask analysisTask graphsHeterogeneous computingOnline algorithm[INFO.INFO-DC]Computer Science [cs]/Distributed Parallel and Cluster Computing [cs.DC]
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