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Journal articles on the topic 'Quantization errors'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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1

Zheng, Dong Xi. "The Realization and Comparison of Directly Fitting Method and Edge Extraction Method Used in Amending the Quantization Errors." Advanced Materials Research 546-547 (July 2012): 537–41. http://dx.doi.org/10.4028/www.scientific.net/amr.546-547.537.

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The quantization error is one of errors in 3D measuring, the method of amending the quantization errors includes directly fitting method and edge extraction method. Analyzed the source of quantization errors and the principle to amend the quantization errors, and analyzed the simulation test of directly fitting method and edge extraction method, and compared them with each other.

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2

Dai, Xinyan, Xiao Yan, Kelvin K. W. Ng, Jiu Liu, and James Cheng. "Norm-Explicit Quantization: Improving Vector Quantization for Maximum Inner Product Search." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 01 (April 3, 2020): 51–58. http://dx.doi.org/10.1609/aaai.v34i01.5333.

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Vector quantization (VQ) techniques are widely used in similarity search for data compression, computation acceleration and etc. Originally designed for Euclidean distance, existing VQ techniques (e.g., PQ, AQ) explicitly or implicitly minimize the quantization error. In this paper, we present a new angle to analyze the quantization error, which decomposes the quantization error into norm error and direction error. We show that quantization errors in norm have much higher influence on inner products than quantization errors in direction, and small quantization error does not necessarily lead to good performance in maximum inner product search (MIPS). Based on this observation, we propose norm-explicit quantization (NEQ) — a general paradigm that improves existing VQ techniques for MIPS. NEQ quantizes the norms of items in a dataset explicitly to reduce errors in norm, which is crucial for MIPS. For the direction vectors, NEQ can simply reuse an existing VQ technique to quantize them without modification. We conducted extensive experiments on a variety of datasets and parameter configurations. The experimental results show that NEQ improves the performance of various VQ techniques for MIPS, including PQ, OPQ, RQ and AQ.

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3

Qin, Li Juan. "Robustness Problem Argumentation from Image Quantization Errors in Vision Location." Advanced Materials Research 225-226 (April 2011): 1332–35. http://dx.doi.org/10.4028/www.scientific.net/amr.225-226.1332.

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In our vision location system, error is inevitable. Image quantization errors play an important role in computer vision field. Quantization errors are the primary sources that affect the precision of pose estimation and they are inherent and unavoidable. It is important to analysis on the effect of this error on compute process. In this paper, Robustness problem argumentation in vision location is presented in detail. Then we introduce image quantization error. Robustness mathematical model for vision location is set up at last.

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4

Ti-Chiun Chang and J. P. Allebach. "Quantization of accumulated diffused errors in error diffusion." IEEE Transactions on Image Processing 14, no. 12 (December 2005): 1960–76. http://dx.doi.org/10.1109/tip.2005.859372.

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5

Vallabha, Gautam K., and Betty Tuller. "Quantization errors in formant estimation." Journal of the Acoustical Society of America 107, no. 5 (May 2000): 2907. http://dx.doi.org/10.1121/1.428820.

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6

Kushner, H. B., M. Meisner, and A. V. Levy. "Almost uniformity of quantization errors." IEEE Transactions on Instrumentation and Measurement 40, no. 4 (1991): 682–87. http://dx.doi.org/10.1109/19.85334.

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7

Stenbakken, G. N., Dong Liu, J. A. Starzyk, and B. C. Waltrip. "Nonrandom quantization errors in timebases." IEEE Transactions on Instrumentation and Measurement 50, no. 4 (2001): 888–92. http://dx.doi.org/10.1109/19.948294.

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8

Xu, De Hong, Huan Xin Peng, and Bin Liu. "Non-Uniform Probabilistically Quantized Distributed Consensus Applied on Sensors Network." Applied Mechanics and Materials 577 (July 2014): 921–25. http://dx.doi.org/10.4028/www.scientific.net/amm.577.921.

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In order to improve the accuracy of distributed consensus under digital communication, in the paper, assuming the initial states of nodes following uniform distribution, a non-uniform quantization scheme based on probabilistic quantization is proposed, and the entire data range is divided based on µ-law non-uniform quantization scheme. The quantization step-size near the average of initial states is smaller, and the corresponding quantization errors are smaller. Base on the proposed quantization scheme, a non-uniform probabilistically quantized distributed consensus algorithm is proposed. The performance and the mean square errors of the non-uniform probabilistically quantized distributed consensus algorithm is analyzed, by analyses and simulations, the results show the non-uniform probabilistically quantized distributed consensus can reach a consensus, and the mean square error is far smaller than that of probabilistically quantized distributed consensus.

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9

Pawlus, Paweł, Rafał Reizer, and Dominik Czach. "The effect of vertical resolution on measurement errors of machined surfaces topography." Mechanik 91, no. 11 (November 12, 2018): 988–91. http://dx.doi.org/10.17814/mechanik.2018.11.177.

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The effect of the quantization error on values of surface topography parameters was examined. Surface topography was measured using an optical profilometer of 0.01 nm vertical resolution. Twenty isotropic and anisotropic, one- and two-process, random and deterministic surfaces were objects of investigations. The vertical resolution was changed using TalyMap software. Tendencies of changes of three surfaces due to quantization errors were analyzed in details. Parameters of the highest and the smallest sensitivity on errors were selected.

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10

Koeck, P. J. B. "Quantization errors in averaged digitized data." Signal Processing 81, no. 2 (February 2001): 345–56. http://dx.doi.org/10.1016/s0165-1684(00)00212-7.

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11

Shykula, Mykola, and Oleg Seleznjev. "Stochastic structure of asymptotic quantization errors." Statistics & Probability Letters 76, no. 5 (March 2006): 453–64. http://dx.doi.org/10.1016/j.spl.2005.08.022.

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12

Shykula, M. "Asymptotic quantization errors for unbounded quantizers." Theory of Probability and Mathematical Statistics 75, no. 00 (January 25, 2008): 189–200. http://dx.doi.org/10.1090/s0094-9000-08-00725-4.

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13

Wong, P. W. "On quantization errors in computer vision." IEEE Transactions on Pattern Analysis and Machine Intelligence 13, no. 9 (1991): 951–56. http://dx.doi.org/10.1109/34.93812.

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14

Yang, Haigen, Linqun Zhu, Zhun Xia, Yanqing Chen, Luohao Dai, Ruotian Xu, YuanHao Chen, et al. "Research on Quantization Error Influence of Millimeter-Wave Phased Array Antenna." International Journal of Antennas and Propagation 2021 (September 24, 2021): 1–19. http://dx.doi.org/10.1155/2021/1874537.

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The millimeter-wave phased array antenna is a higher integration system that is composed of different subarray modules, and in actual engineering, the existing amplitude, phase errors, and structural errors will change the performance of the array antenna. This paper studies the influence of the random amplitude and phase errors of the antenna array in the actual assembly process and the actual position errors between the subarrays on the electrical performance of the antenna. Based on the planar rectangular antenna array-electromagnetic coupling model, we propose a method of verifying the effect of random errors on the phased array antenna. The simulation result shows that the method could obtain the critical value of the error generated by the antenna subarray during processing and assembly. To reduce the error factor, it is necessary to ensure that the random phase and amplitude error should not exceed 10 ° , 0.5 dB . The error in the X-direction during assembly should be ≤ 0.05 λ , and the error in the Y-direction should be ≤ 0.1 λ . When symmetrical deformation occurs, the maximum deformation should be less than 0.05 λ .

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15

GRAF, SIEGFRIED, HARALD LUSCHGY, and GILLES PAGÈS. "Fractal functional quantization of mean-regular stochastic processes." Mathematical Proceedings of the Cambridge Philosophical Society 150, no. 1 (June 22, 2010): 167–91. http://dx.doi.org/10.1017/s0305004110000344.

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AbstractWe investigate the functional quantization problem for stochastic processes with respect toLp(IRd, μ)-norms, where μ is a fractal measure namely, μ is self-similar or a homogeneous Cantor measure. The derived functional quantization upper rate bounds are universal depending only on the mean-regularity index of the process and the quantization dimension of μ and as universal rates they are optimal. Furthermore, for arbitrary Borel probability measures μ we establish a (nonconstructive) link between the quantization errors of μ and the functional quantization errors of the process in the spaceLp(IRd, μ).

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16

Jimenez, David, Long Wang, and Yang Wang. "White Noise Hypothesis for Uniform Quantization Errors." SIAM Journal on Mathematical Analysis 38, no. 6 (January 2007): 2042–56. http://dx.doi.org/10.1137/050636929.

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17

Liu, Feng, Eze Ahanonu, Michael W. Marcellin, Yuzhang Lin, Amit Ashok, and Ali Bilgin. "Visibility of quantization errors in reversible JPEG2000." Signal Processing: Image Communication 84 (May 2020): 115812. http://dx.doi.org/10.1016/j.image.2020.115812.

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18

Bugrov, V. "Dynamic Quantization of Digital Filter Coefficients." Proceedings of Telecommunication Universities 7, no. 2 (June 30, 2021): 8–17. http://dx.doi.org/10.31854/1813-324x-2021-7-2-8-17.

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The possibility of quantizing the coefficients of a digital filter in the concept of dynamic mathematical programming, as a dynamic process of step-by-step quantization of coefficients with their discrete optimization at each step according to the objective function, common to the entire quantization process, is considered. Dynamic quantization can significantly reduce the functional error when implementing the required characteristics of a lowbit digital filter in comparison with classical quantization. An algorithm is presented for step-by-step dynamic quantization using integer nonlinear programming methods, taking into account the specified signal scaling and the radius of the poles of the filter transfer function. The effectiveness of this approach is illustrated by dynamically quantizing the coefficients of a cascaded high-order IIR bandpass filter with a minimum bit depth to represent integer coefficients. A comparative analysis of functional quantization errors is carried out, as well as a test of the quantized filter performance on test and real signals.

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19

Rosenblatt, Joseph, and Mrinal Kanti Roychowdhury. "Optimal Quantization for Piecewise Uniform Distributions." Uniform distribution theory 13, no. 2 (December 1, 2018): 23–55. http://dx.doi.org/10.2478/udt-2018-0009.

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Abstract Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite number of points. In this paper, firstly a general approach to this process is outlined using independent random variables and ergodic maps; these give asymptotically the optimal sets of n-means and the nth quantization errors for all positive integers n. Secondly two piecewise uniform distributions are considered on R: one with infinite number of pieces and one with finite number of pieces. For these two probability measures, we describe the optimal sets of n-means and the nth quantization errors for all n ∈ N. It is seen that for a uniform distribution with infinite number of pieces to determine the optimal sets of n-means for n ≥ 2 one needs to know an optimal set of (n − 1)-means, but for a uniform distribution with finite number of pieces one can directly determine the optimal sets of n-means and the nth quantization errors for all n ∈ N.

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20

Goto, Yutaka. "Effects of Noise on the Interpolation Accuracy for Apodized FFT Spectra of Time-Domain Damped Signals." Applied Spectroscopy 49, no. 12 (December 1995): 1776–80. http://dx.doi.org/10.1366/0003702953966037.

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Interpolation formulas for the apodized magnitude-mode fast Fourier transformed (FFT) spectra determine accurately the frequency, damping constant, and amplitude of time-domain damped signals. However, additive noise causes a large amount of error in interpolation. In this paper, we obtain, theoretically, the frequency-domain signal-to-noise (S/N) ratio due to windowing by the function of sinα( X) and quantization with finite bit-length analog-to-digital (A/D) converters. Then, with the use of the squared ratios between three magnitudes nearest to the peak maximum on the apodized FFT spectrum, we derive the relationship equation between the frequency error and the S/N ratio. The results obtained by computer simulation of experimental conditions (i.e., sampling, quantization, windowing, FFT, and interpolation) for the Hanning window (α = 2) agree well with the theoretical calculations; the frequency errors decrease with increasing bit-length of the A/D converter. These observed errors are unavoidable because A/D converters are indispensable for measurements with Fourier transform spectrometers. Furthermore, as shown theoretically, the observed accuracy of interpolation is inversely proportional to the S/N ratio, provided that the S/N ratio is below the value due to quantization and windowing.

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21

Viswanathan, H., and R. Zamir. "On the whiteness of high-resolution quantization errors." IEEE Transactions on Information Theory 47, no. 5 (July 2001): 2029–38. http://dx.doi.org/10.1109/18.930935.

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22

Sidor, Tadeusz. "METROLOGICAL PROPERTIES OF A/D CONVERTERS UTILIZING HIGHER ORDER SIGMA–DELTA MODULATORS COMPARED WITH A/D CONVERTERS WITH MODULATORS OF FIRST ORDER." Metrology and Measurement Systems 21, no. 1 (March 1, 2014): 37–46. http://dx.doi.org/10.2478/mms-2014-0004.

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Abstract Time domain analysis is used to determine whether A/D converters that employ higher order sigma-delta modulators, widely used in digital acoustic systems, have superior performance over classical synchronous A/D converters with modulators of first order when taking into account their important metrological property which is the magnitude of the quantization error. It is shown that the quantization errors of delta-sigma A/D converters with higher order modulators are exactly on the same level as for converters with a first order modulator.

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23

Mena-Parra, J., K. Bandura, M. A. Dobbs, J. R. Shaw, and S. Siegel. "Quantization Bias for Digital Correlators." Journal of Astronomical Instrumentation 07, no. 02n03 (September 2018): 1850008. http://dx.doi.org/10.1142/s2251171718500083.

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In radio interferometry, the quantization process introduces a bias in the magnitude and phase of the measured correlations which translates into errors in the measurement of source brightness and position in the sky, affecting both the system calibration and image reconstruction. In this paper, we investigate the biasing effect of quantization in the measured correlation between complex-valued inputs with a circularly symmetric Gaussian probability density function (PDF), which is the typical case for radio astronomy applications. We start by calculating the correlation between the input and quantization error and its effect on the quantized variance, first in the case of a real-valued quantizer with a zero mean Gaussian input and then in the case of a complex-valued quantizer with a circularly symmetric Gaussian input. We demonstrate that this input-error correlation is always negative for a quantizer with an odd number of levels, while for an even number of levels, this correlation is positive in the low signal level regime. In both cases, there is an optimal interval for the input signal level for which this input-error correlation is very weak and the model of additive uncorrelated quantization noise provides a very accurate approximation. We determine the conditions under which the magnitude and phase of the measured correlation have negligible bias with respect to the unquantized values: we demonstrate that the magnitude bias is negligible only if both unquantized inputs are optimally quantized (i.e. when the uncorrelated quantization error model is valid), while the phase bias is negligible when (1) at least one of the inputs is optimally quantized, or when (2) the correlation coefficient between the unquantized inputs is small. Finally, we determine the implications of these results for radio interferometry.

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24

Graf and Luschgy. "ASYMPTOTICS OF THE QUANTIZATION ERRORS FOR SELF-SIMILAR PROBABILITIES." Real Analysis Exchange 26, no. 2 (2000): 795. http://dx.doi.org/10.2307/44154078.

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25

Srinivasan, Sriram, Ashish Pandharipande, and Kees Janse. "Beamforming under Quantization Errors in Wireless Binaural Hearing Aids." EURASIP Journal on Audio, Speech, and Music Processing 2008 (2008): 1–8. http://dx.doi.org/10.1155/2008/824797.

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26

Zhiheng Li, Yudong Chen, Li Li, and Yi Zhang. "Quantization Errors of Uniformly Quantized fGn and fBm Signals." IEEE Signal Processing Letters 16, no. 12 (December 2009): 1059–62. http://dx.doi.org/10.1109/lsp.2009.2030115.

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27

Wang, Yang. "Sigma–delta quantization errors and the traveling salesman problem." Advances in Computational Mathematics 28, no. 2 (March 28, 2007): 101–18. http://dx.doi.org/10.1007/s10444-006-9016-1.

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28

Diamond, P., and I. Vladimirov. "Asymptotic Independence and Uniform Distribution of Quantization Errors for Spatially Discretized Dynamical Systems." International Journal of Bifurcation and Chaos 08, no. 07 (July 1998): 1479–90. http://dx.doi.org/10.1142/s0218127498001133.

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Computer simulation of dynamical systems involves a state space which is the finite set of computer arithmetic. Restricting state values to this grid produces roundoff effects which can be studied by replacing the original system with a spatially discretized dynamical system. Study of the deviation of the discretized trajectories from those of the original system reduces to that of appropriately defined quantization errors. As the grid is refined, the asymptotic behavior of these quantization errors follows probabilistic laws. These results are applied to discretized polynomial mappings of the unit interval.

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29

Ivanis, Predrag, and Dusan Drajic. "Adaptive vector quantization in SVD MIMO system backward link with limited number of active sub channels." Serbian Journal of Electrical Engineering 1, no. 3 (2004): 113–23. http://dx.doi.org/10.2298/sjee0403113i.

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This paper presents combination of Channel Optimized Vector Quantization based on LBG algorithm and sub channel power allocation for MIMO systems with Singular Value Decomposition and limited number of active sub channels. Proposed algorithm is designed to enable maximal throughput with bit error rate bellow some tar- get level in case of backward channel capacity limitation. Presence of errors effect in backward channel is also considered.

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30

Jin, Yongseok, Jinsung Kim, and Hyuk-Jae Lee. "Reduction of quantization errors caused by dynamic LCD backlight scaling." IEICE Electronics Express 6, no. 9 (2009): 535–39. http://dx.doi.org/10.1587/elex.6.535.

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31

Jenkin, R., R. E. Jacobson, and M. A. Richardson. "Errors due to quantization in MTF determination using sinusoidal targets." Imaging Science Journal 53, no. 3 (September 2005): 140–48. http://dx.doi.org/10.1179/136821905x50325.

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32

Neuhoff, D. L. "On the asymptotic distribution of the errors in vector quantization." IEEE Transactions on Information Theory 42, no. 2 (March 1996): 461–68. http://dx.doi.org/10.1109/18.485716.

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33

Rao, D. "Analysis of coefficient quantization errors in state-space digital filters." IEEE Transactions on Acoustics, Speech, and Signal Processing 34, no. 1 (February 1986): 131–39. http://dx.doi.org/10.1109/tassp.1986.1164793.

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34

Zakhor, A., and A. Oppenheim. "Quantization errors in the computation of the discrete Hartley transform." IEEE Transactions on Acoustics, Speech, and Signal Processing 35, no. 11 (November 1987): 1592–602. http://dx.doi.org/10.1109/tassp.1987.1165074.

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35

Wagdy, Mahmoud Fawzy. "Effect of ADC quantization errors on some periodic signal measurements." IEEE Transactions on Instrumentation and Measurement IM-36, no. 4 (December 1987): 983–89. http://dx.doi.org/10.1109/tim.1987.6312595.

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36

Tyrsa, V. E. "Instrumental errors in time interval measurements by difference-period quantization." Measurement Techniques 29, no. 6 (June 1986): 565–68. http://dx.doi.org/10.1007/bf00865823.

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37

Smagin, Vladimir A., Vladimir P. Bubnov, and Shokhrukh K. Sultonov. "Mathematical models for calculating the quantitative characteristics of the optimal quantization of information." Transportation Systems and Technology 7, no. 1 (March 31, 2021): 46–58. http://dx.doi.org/10.17816/transsyst20217146-58.

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Various additional mathematical aspects related to solving the problem of optimal information quantization in the sense of filling are considered, such as control of quantum elements, accounting for errors of quantum elements, determining the amount of information during quantization, and determining the numerical values of fractals of distributions represented as a sequential fractal distribution. The purpose of the article is to consider additional questions based on a specific "heavy" probability distribution the normal distribution. The considered questions are made in order to facilitate the solution of applied problems for researchers dealing with the problem of information quantization.

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38

Chen, Hao, You Peng You, Jun He, and Xue Feng Yang. "A Separated-Axis Interpolator with Variable Period for Stepping Systems." Key Engineering Materials 431-432 (March 2010): 61–64. http://dx.doi.org/10.4028/www.scientific.net/kem.431-432.61.

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In motion systems driven by stepping motors, reference word interpolation is usually used with a constant period T, in which the existing position quantization errors will inevitably result in the trouble of velocity quantization errors. A separated-axis interpolator with variable period is proposed to deal with these troubles. The reassignment module of displacement and time is the key of the interpolator. In the module, the interpolation period of each axis can be separately adjusted upon its quantized displacement, thus resulting in almost ideal velocity profile and moving smoothness. Simulation and machining results are given and show that the proposed interpolator is effective in the improvement of motion stability and interpolation accuracy.

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39

Kim, Cheonshik, Dong-Kyoo Shin, Ching-Nung Yang, and Lu Leng. "Hybrid Data Hiding Based on AMBTC Using Enhanced Hamming Code." Applied Sciences 10, no. 15 (August 2, 2020): 5336. http://dx.doi.org/10.3390/app10155336.

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The image-based data hiding method is a technology used to transmit confidential information secretly. Since images (e.g., grayscale images) usually have sufficient redundancy information, they are a very suitable medium for hiding data. Absolute Moment Block Truncation Coding (AMBTC) is one of several compression methods and is appropriate for embedding data due to its very low complexity and acceptable distortion. However, since there is not enough redundant data compared to grayscale images, the research to embed data in the compressed image is a very challenging topic. That is the motivation and challenge of this research. Meanwhile, the Hamming codes are used to embed secret bits, as well as a block code that can detect up to two simultaneous bit errors and correct single bit errors. In this paper, we propose an effective data hiding method for two quantization levels of each block of AMBTC using Hamming codes. Bai and Chang introduced a method of applying Hamming (7,4) to two quantization levels; however, the scheme is ineffective, and the image distortion error is relatively large. To solve the problem with the image distortion errors, this paper introduces a way of optimizing codewords and reducing pixel distortion by utilizing Hamming (7,4) and lookup tables. In the experiments, when concealing 150,000 bits in the Lena image, the averages of the Normalized Cross-Correlation (NCC) and Mean-Squared Error (MSE) of our proposed method were 0.9952 and 37.9460, respectively, which were the highest. The sufficient experiments confirmed that the performance of the proposed method is satisfactory in terms of image embedding capacity and quality.

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40

Zhu, Xiaolong, Sitong Xiang, and Jianguo Yang. "Novel thermal error modeling method for machining centers." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 8 (July 28, 2014): 1500–1508. http://dx.doi.org/10.1177/0954406214545661.

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Thermal deformation is one of the main contributors to machining errors in machine tools. In this paper, a novel approach to build an effective thermal error model for a machining center is proposed. Adaptive vector quantization network clustering algorithm is conducted to identify the temperature variables, and then one temperature variable is selected from each cluster to represent the same cluster. Furthermore, a non-linear model based on output-hidden feedback Elman neural network is adopted to establish the relationship between thermal error and temperature variables. The output-hidden feedback Elman network is adopted to predict the thermal deformation of the machining center. Back propagation (BP) neural network is introduced for comparison. A verification experiment on the machining center is carried out to validate the efficiency of the newly proposed method. Experimental verification shows that the adaptive vector quantization network clustering algorithm and output-hidden feedback Elman neural network is an accurate and effective method.

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41

Peng, Huan Xin, Wen Kai Wang, and Bin Liu. "Pseudo Two-Hop Distributed Consensus with Adaptive Quantization." Advanced Materials Research 889-890 (February 2014): 662–65. http://dx.doi.org/10.4028/www.scientific.net/amr.889-890.662.

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In order to improve the accuracy and the convergence rate of distributed consensus under quantized communication, in the paper, based on adaptive quantization scheme, we propose the pseudo two-hop distributed consensus algorithm. By analyses and simulations, Results show that the pseudo two-hop distributed consensus algorithm based on adaptive quantization can reach an average consensus, and its convergence rate is higher than that of the first-order adaptive quantized distributed consensus algorithm, moreover, the mean square errors are smaller within the finite steps.

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42

Feng, Yifu, Zhi-Min Li, and Xiao-Heng Chang. "H∞ Filtering for Discrete-Time Nonlinear Singular Systems with Quantization." Mathematical Problems in Engineering 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/9548407.

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This paper investigates the problem of H∞ filtering for class discrete-time Lipschitz nonlinear singular systems with measurement quantization. Assume that the system measurement output is quantized by a static, memoryless, and logarithmic quantizer before it is transmitted to the filter, while the quantizer errors can be treated as sector-bound uncertainties. The attention of this paper is focused on the design of a nonlinear quantized H∞ filter to mitigate quantization effects and ensure that the filtering error system is admissible (asymptotically stable, regular, and causal), while having a unique solution with a prescribed H∞ noise attenuation level. By introducing some slack variables and using the Lyapunov stability theory, some sufficient conditions for the existence of the nonlinear quantized H∞ filter are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is presented to demonstrate the effectiveness of the proposed quantized filter design method.

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SATO, Hiroshi, and Kensei EHARA. "Determination of Uncertainty Associated with Quantization Errors Using the Bayesian Approach." Transactions of the Society of Instrument and Control Engineers 43, no. 7 (2007): 536–42. http://dx.doi.org/10.9746/ve.sicetr1965.43.536.

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44

Sheikh, Alireza, Christoffer Fougstedt, Alexandre Graell i. Amat, Pontus Johannisson, Per Larsson-Edefors, and Magnus Karlsson. "Dispersion Compensation FIR Filter With Improved Robustness to Coefficient Quantization Errors." Journal of Lightwave Technology 34, no. 22 (November 15, 2016): 5110–17. http://dx.doi.org/10.1109/jlt.2016.2599276.

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45

Hsieh, H., and Chia-Liang Lin. "Spectral Shaping of Dithered Quantization Errors in Sigma–Delta Modulators." IEEE Transactions on Circuits and Systems I: Regular Papers 54, no. 5 (May 2007): 974–80. http://dx.doi.org/10.1109/tcsi.2007.895511.

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46

RIZZO, F., J. STORER, and B. CARPENTIERI. "Overlap and channel errors in Adaptive Vector Quantization for image coding." Information Sciences 171, no. 1-3 (March 4, 2005): 125–43. http://dx.doi.org/10.1016/j.ins.2004.03.020.

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Lang, Xiaoyu, Christopher J. Damaren, and Xibin Cao. "Passivity-based attitude control with input quantization." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 4 (February 5, 2018): 1546–51. http://dx.doi.org/10.1177/0954410017754018.

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A passivity-based controller with quantization for spacecraft attitude control is developed. This passive control scheme includes two parts which are a proportional controller for quaternion feedback and a strictly positive real controller for the angular velocity. To alleviate the errors caused by quantization, a special modification for the nonlinear quantized input is employed in the strictly positive real controller. Asymptotic stability can be guaranteed with the presented controller structure. A guideline for the controller parameter selection is provided with sensitivity analysis for the control scheme. Numerical simulation results demonstrate the effectiveness of the proposed controller.

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Liu, Jingyu, Qiong Wang, Dunbo Zhang, and Li Shen. "Super-Resolution Model Quantized in Multi-Precision." Electronics 10, no. 17 (September 6, 2021): 2176. http://dx.doi.org/10.3390/electronics10172176.

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Deep learning has achieved outstanding results in various tasks in machine learning under the background of rapid increase in equipment’s computing capacity. However, while achieving higher performance and effects, model size is larger, training and inference time longer, the memory and storage occupancy increasing, the computing efficiency shrinking, and the energy consumption augmenting. Consequently, it’s difficult to let these models run on edge devices such as micro and mobile devices. Model compression technology is gradually emerging and researched, for instance, model quantization. Quantization aware training can take more accuracy loss resulting from data mapping in model training into account, which clamps and approximates the data when updating parameters, and introduces quantization errors into the model loss function. In quantization, we found that some stages of the two super-resolution model networks, SRGAN and ESRGAN, showed sensitivity to quantization, which greatly reduced the performance. Therefore, we use higher-bits integer quantization for the sensitive stage, and train the model together in quantization aware training. Although model size was sacrificed a little, the accuracy approaching the original model was achieved. The ESRGAN model was still reduced by nearly 67.14% and SRGAN model was reduced by nearly 68.48%, and the inference time was reduced by nearly 30.48% and 39.85% respectively. What’s more, the PI values of SRGAN and ESRGAN are 2.1049 and 2.2075 respectively.

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Molytė, Alma, and Olga Kurasova. "Vektorių kvantavimo metodų ir daugiamačių skalių junginys daugiamačiams duomenims vizualizuoti." Informacijos mokslai 50 (January 1, 2009): 340–46. http://dx.doi.org/10.15388/im.2009.0.3215.

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Darbe pateikiama lyginamoji dviejų vektorių kvantavimo metodų (saviorganizuojančių neuroninių tinklų ir neuroninių dujų) analizė. Neuronai nugalėtojai, kurie gaunami vektorių kvantavimo metodais, yra vizualizuojami daugiamačių skalių metodu. Tirta kvantavimo paklaidos priklausomybė nuo vektorių nugalėtojų skaičiaus. Išsiaiškinta, kuris vektorių kvantavimo metodas yra tinkamesnis jungti su daugiamačių skalių metodu, t. y. vizualizavus neuronus nugalėtojus „atskleidžiama“ analizuojamųduomenų struktūra.Combination of Vector Quantization and Multidimensional ScalingAlma Molytė, Olga Kurasova SummaryIn this paper, we present a comparative analysis of a combination of two vector quantization methods (self-organizing map (SOM) and neural gas (NG)), based on neural networks and multidimensional scaling that is used for visualization of codebook vectors obtained by vector quantization methods. The dependence of neuron-winners, quantization and mapping qualities, and preserving of a data structure in the mapping image are investigated. It is established that the quantization errors of NG are smaller than that of the SOM when the number of neurons-winners is approximately equal. It means that the neural gas is more suitable for vector quantization. The data structure is visible in the mapping image even when the number r of neurons-winners of NG is small enough. If the number r of neurons-winners of the SOM is larger, the data structure is visible, as well.8px;">

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Wu, Tao, Hao Fu, Bokai Liu, Hanzhang Xue, Ruike Ren, and Zhiming Tu. "Detailed Analysis on Generating the Range Image for LiDAR Point Cloud Processing." Electronics 10, no. 11 (May 21, 2021): 1224. http://dx.doi.org/10.3390/electronics10111224.

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Range images are commonly used representations for 3D LiDAR point cloud in the field of autonomous driving. The approach of generating a range image is generally regarded as a standard approach. However, there do exist two different types of approaches to generating the range image: In one approach, the row of the range image is defined as the laser ID, and in the other approach, the row is defined as the elevation angle. We named the first approach Projection By Laser ID (PBID), and the second approach Projection By Elevation Angle (PBEA). Few previous works have paid attention to the difference of these two approaches. In this work, we quantitatively analyze these two different approaches. Experimental results show that the PBEA approach can obtain much smaller quantization errors than PBID, and should be the preferred choice in reconstruction-related tasks. If PBID is chosen for use in recognition-related tasks, then we have to tolerate its larger quantization error.

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