Relevant bibliographies by topics / Electronic noise – Mathematical models

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Electronic noise – Mathematical models'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "Electronic noise – Mathematical models"

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Jondral, Friedrich K. "White Gaussian Noise – Models for Engineers." Frequenz 72, no. 5-6 (April 25, 2018): 293–99. http://dx.doi.org/10.1515/freq-2017-0064.

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AbstractThis paper assembles some information about white Gaussian noise (WGN) and its applications. It starts from a description of thermal noise, i. e. the irregular motion of free charge carriers in electronic devices. In a second step, mathematical models of WGN processes and their most important parameters, especially autocorrelation functions and power spectrum densities, are introduced. In order to proceed from mathematical models to simulations, we discuss the generation of normally distributed random numbers. The signal-to-noise ratio as the most important quality measure used in communications, control or measurement technology is accurately introduced. As a practical application of WGN, the transmission of quadrature amplitude modulated (QAM) signals over additive WGN channels together with the optimum maximum likelihood (ML) detector is considered in a demonstrative and intuitive way.
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Fedorko, Gabriel, David Heinz, Vieroslav Molnár, and Tomáš Brenner. "Use of mathematical models and computer software for analysis of traffic noise." Open Engineering 10, no. 1 (March 10, 2020): 129–39. http://dx.doi.org/10.1515/eng-2020-0021.

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AbstractNoise measurement and evaluation of the existing noise situation is carried out in the vicinity of selected roads to demonstrate the need for the design of anti-noise measures or to assess the effectiveness of the measures. The selection and number of measuring points, time and intervals, the road noise measurement procedure and the measuring instruments used shall be used in accordance with the provisions of the STN ISO 1996-1 and STN ISO 1996-2 standards. During the measurement, it is also necessary to determine the microclimatic conditions of measurement, such as temperature and relative humidity, wind direction and speed, barometric pressure, duration and intensity of precipitation at the measuring point. The determinant for the definition of road traffic noise is the equivalent sound level A or the equivalent sound level in the third octave bands over a given time interval. In specific cases, it is possible to determine the equivalent sound pressure level from individual vehicle transit.
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Riabukha, V. P., A. V. Semeniaka, and Ye A. Katiushyn. "Mathematical Models of Cross-Correlated and Uncorrelated Gaussian Noise Jamming from External Sources." Radioelectronics and Communications Systems 64, no. 3 (March 2021): 147–54. http://dx.doi.org/10.3103/s0735272721030043.

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Szupiluk, Ryszard, and Tomasz Ząbkowski. "EGLD system for noise identification in ensemble predictors." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 33, no. 6 (October 28, 2014): 2006–15. http://dx.doi.org/10.1108/compel-11-2013-0354.

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Purpose – The purpose of this paper is to propose a noise identification method for data without temporal structure, in which application of typical mathematical white or colored noise models is very limited due to observation order requirements. The method is used to identify the destructive elements and to eliminate them what finally brings prediction improvement. Design/methodology/approach – The paper concerns noise detection problem presented in the framework of ensemble methods via blind signals separation. The authors utilize the Extended Generalized Lambda Distribution (EGLD) model to compare the signals with the target. Findings – The authors proposed novel signals similarity measure which is based on the EGLD system. The authors showed that it can be applied for data with or without time structure, as well as for data which are mutually uncorrelated. It turned out that method is effective for noise identification and can be an alternative, in many cases, to correlation approach, particularly for noise identification problems. Originality/value – In this method the improvement of prediction results is associated with elimination of the real physical factors rather than mathematical averaging in terms of arbitrary assumed distributions. In this approach, it does not matter what is the structure of aggregated models, what significantly distinct this approach from such techniques as boosting or bagging, in which the aggregation process applies to the models of similar structure. For this reason the methodology is focussed on physical noises elimination from predictions and it is complementary to the other ensemble approaches.
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Lau, D. L., R. Ulichney, and G. R. Arce. "Blue- and green-noise halftoning models." IEEE Signal Processing Magazine 20, no. 4 (July 2003): 28–38. http://dx.doi.org/10.1109/msp.2003.1215229.

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Xue, Xiao Min, Qing Sun, and Xiao Hong Wu. "Anti-Noise Simulation of the Hysteresis Mathematic Model Using Computationally-Efficient GA." Applied Mechanics and Materials 226-228 (November 2012): 725–28. http://dx.doi.org/10.4028/www.scientific.net/amm.226-228.725.

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Hysteresis is a particular feature of a wide range of physical systems and devices such as electromagnetic fields, mechanical stress–strain elements and electronic relay circuits. The extended Bouc-Wen model is one of the most widely used hysteresis models in mechanics. It has the capability to emulate the behavior of a wide class of hysteretic systems. However multi parameters have plagued its further application because the capability of computer and algorithm available currently can not meet the need completely. Thus to exploit an effective parallel algorithm is very essential. This paper is committed to propose a novel Genetic Algorithm (GA) so as to identify the parameters of the Bouc-Wen model with noise disturbance efficiently and accurately. Finally a large amount of noise-involved experimental data obtained from a real MR damper is employed to verify the proposed approach has the capability to estimate the satisfactory parameters of the Bouc-Wen model. Also suggested are the implications of the present study on other nonlinear hysteretic models or other complex mathematical models.
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Piazza, Alfredo J., and Can E. Korman. "Computation of the Spectral Density of Current Fluctuations in Bulk Silicon Based on the Solution of the Boltzmann Transport Equation." VLSI Design 6, no. 1-4 (January 1, 1998): 185–89. http://dx.doi.org/10.1155/1998/75094.

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Numerical simulation results for the spectral density of noise due to current fluctuations are presented. The mathematical framework is based on the interpretation of the equations describing electron transport in the semiclassical transport model as stochastic differential equations (SDE). Within this framework, it was previously shown that the autocovariance function of current fluctuations can be obtained from the transient solution of the Boltzmann transport equation (BTE) with special initial conditions. The key aspect which differentiates this approach from other noise models is that this approach directly connects noise characteristics with the physics of scattering in the semiclassical transport model and makes no additional assumptions regarding the nature of noise. The solution of the BTE is based on the Legendre polynomial method. A numerical algorithm is presented for the solution of the transient BTE. Numerical results are in good agreement with Monte Carlo noise simulations for the spectral density of current fluctuations in bulk silicon.
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CAVIN, RALPH K., VICTOR V. ZHIRNOV, JAMES A. HUTCHBY, and GEORGE I. BOURIANOFF. "ENERGY BARRIERS, DEMONS, AND MINIMUM ENERGY OPERATION OF ELECTRONIC DEVICES." Fluctuation and Noise Letters 05, no. 04 (December 2005): C29—C38. http://dx.doi.org/10.1142/s0219477505002951.

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The presence of thermal noise dictates that an energy barrier is needed to preserve a binary state. Therefore, all electronic devices contain at least one energy barrier to control electron flow. The barrier properties determine the operating characteristics of electronic devices. Furthermore, changes in the barrier shape require changes in charge density. Operation of all charge transport devices includes charging/discharging capacitances to change barrier height. We analyze energy dissipation for several schemes of charging capacitors. A basic assumption of Reversible Computing is that the computing system is completely isolated from the thermal bath. An isolated system is a mathematical abstraction never perfectly realized in practice. Errors due to thermal excitations are equivalent to information erasure, and thus computation dissipates energy. Another source of energy dissipation is due to the need of measurement and control. To analyze this side of the problem, the Maxwell's Demon is a useful abstraction. We hold that apparent "energy savings" in models of adiabatic circuits result from neglecting the total energy needed by other parts of the system to implement the circuit.
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Kumar, K., D. Yadav, and B. V. Srinivas. "Adaptive noise models for extended Kalman filter." Journal of Guidance, Control, and Dynamics 14, no. 2 (March 1991): 475–77. http://dx.doi.org/10.2514/3.20665.

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Shi-Xiong Zhang, Anton Ragni, and Mark John Francis Gales. "Structured Log Linear Models for Noise Robust Speech Recognition." IEEE Signal Processing Letters 17, no. 11 (November 2010): 945–48. http://dx.doi.org/10.1109/lsp.2010.2077626.

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Dissertations / Theses on the topic "Electronic noise – Mathematical models"

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Tomlin, Toby-Daniel. "Analysis and modelling of jitter and phase noise in electronic systems : phase noise in RF amplifiers and jitter in timing recovery circuits." University of Western Australia. School of Electrical, Electronic and Computer Engineering, 2004. http://theses.library.uwa.edu.au/adt-WU2004.0021.

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Timing jitter and phase noise are important design considerations in most electronic systems, particularly communication systems. The desire for faster transmission speeds and higher levels of integration, combined with lower signal levels and denser circuit boards has placed greater emphasis on managing problems related to phase noise, timing jitter, and timing distribution. This thesis reports original work on phase noise modelling in electronic systems. A new model is proposed which predicts the up-conversion of baseband noise to the carrier frequency in RF amplifiers. The new model is validated by comparing the predicted phase noise performance to experimental measurements as it applies to a common emitter (CE), bipolar junction transistor (BJT) amplifier. The results show that the proposed model correctly predicts the measured phase noise, including the shaping of the noise about the carrier frequency, and the dependence of phase noise on the amplifier parameters. In addition, new work relating to timing transfer in digital communication systems is presented. A new clock recovery algorithm is proposed for decoding timing information encoded using the synchronous residual time-stamp (SRTS) method. Again, theoretical analysis is verified by comparison with an experimental implementation. The results show that the new algorithm correctly recovers the source clock at the destination, and satisfies the jitter specification set out by the ITU-T for G.702 signals.
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Chun, Sungjun. "Methodologies for modeling simultaneous switching noise in multi-layered packages and boards." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/15452.

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Kumar, Neraj. "Detection of Variable Retention Time in DRAM." PDXScholar, 2014. https://pdxscholar.library.pdx.edu/open_access_etds/2103.

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This thesis investigates a test method to detect the presence of Variable Retention Time (VRT) bits in manufactured DRAM. The VRT bits retention time is modeled as a 2-state random telegraph process that includes miscorrelation between test and use. The VRT defect is particularly sensitive to test and use conditions. A new test method is proposed to screen the VRT bits by simulating the use conditions during manufacturing test. Evaluation of the proposed test method required a bit-level VRT model to be parameterized as a function of temperature and voltage conditions. The complete 2-state VRT bit model combines models for the time-in-state and for the retention-time including miscorrelation. A copula is used to model the eect of miscorrelation between test and use. The proposed VRT test algorithm runtime is estimated as a function of VRT test coverage, test temperature and test voltage.
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Luo, Yan, and 罗妍. "Three essays on noise and institutional trading." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44549246.

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Taylor, Katherine P. "Noise models of A/D and D/A converters for determination of fundamental noise limitations." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/16910.

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Envia, Edmane. "Influence of vane sweep on rotor-stator interaction noise." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184609.

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In this dissertation the influence of vane sweep on rotor-stator interaction noise is investigated. In an analytical approach, the interaction of a convected gust, representing the rotor viscous wake, with a cascade of finite span swept airfoils, representing the stator, is analyzed. The analysis is based on the solution of the exact linearized equations of motion. High-frequency convected gusts for which noise generation is concentrated near the leading edge of the airfoils are considered. In a preliminary study, the problem of an isolated finite span swept airfoil interacting with a convected gust is analyzed. Using Fourier transform methods and the Wiener-Hopf technique, an approximate solution for this problem is developed. Closed form expressions for the acoustic farfield are obtained and used in a parametric study to assess the effect of airfoil sweep on noise generation. Results indicate that sweep can substantially reduce the farfield noise levels for a single airfoil. Utilizing the single airfoil model, an approximate solution to the problem of noise radiation from a cascade of finite span swept airfoils interacting with a convected gust is derived. Only upstream radiated noise is considered. Neglecting the weak coupling between the adjacent leading edges at high frequencies, the cascade solution is constructed as a superposition of acoustic farfields emanating from an infinite number of isolated airfoils. A parametric study of noise generated by gust-cascade interaction is then carried out to assess the effectiveness of vane sweep in reducing rotor-stator interaction noise. The results of the parametric study show that, over a fairly wide range of conditions, sweep is beneficial in reducing noise levels. One conclusion of particular importance is that rotor wake twist or circumferential lean substantially influences the effectiveness of vane sweep. The orientation of the vane sweep must be chosen to enhance the natural phase lag caused by wake lean, in which case rather small sweep angles substantially reduce the noise levels.
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Mackenzie, Neil C. "The independent quadratic optimisation algorithm for the active control of noise and vibration /." Title page, contents and abstract only, 1996. http://web4.library.adelaide.edu.au/theses/09PH/09phm15742.pdf.

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DITOLLA, ROBERT JOHN. "RANDOM VIBRATION ANALYSIS BY THE POWER SPECTRUM AND RESPONSE SPECTRUM METHODS (WHITE NOISE, FINITE-ELEMENT, VANMARCKE, DENSITY, NASTRAN)." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/183836.

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Determination of the stresses and displacements which occur in response to random excitations cannot be accomplished by traditional deterministic analysis methods. As the specification of the excitation and the response of the structure become more complex, solutions by direct, closed-form methods require extensive computations. Two methods are presented which can be used in the analysis of structures which are subjected to random excitations. The Power Spectrum Method is a procedure which determines the random vibration response of the structure based upon a frequency response analysis of a structural model. The Response Spectrum Method is a method which is based upon specified forces or displacements as a function of time. A derivation of each of the methods is presented and followed by comparisons of the results which were obtained for single and multiple-degree-of-freedom systems. Assumptions and limitations of the methods are discussed as well as their accuracy over ranges of frequency, damping and loading specification. As a direct application and comparison of the two methods, an analysis of the support system for the primary mirror of the Space Infrared Telescope Facility (SIRTF) has been performed. In addition, a method for the evaluation of the critical damping in a single-degree-of-freedom structure is demonstrated.
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Hinkle, Adam R. "Tight-binding calculation of electronic properties of oligophenyl and oligoacene nanoribbons." Virtual Press, 2008. http://liblink.bsu.edu/uhtbin/catkey/1398716.

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Within recent years, allotropic structures of carbon have been produced in the forms of tubes and ribbons which offer the promise of extraordinary electronic and thermal properties. Here we present analyses of oligophenyl and oligoacene systems–infinite, one-dimensional chains of benzene rings linked along the armchair and zigzag directions. These one-dimensional structures, which are amenable to calculation by analytical means, exhibit features very similar to carbon nanotubes and nanoribbons. Using a tight-binding Hamiltonian we analytically determine the density of states, local density of states, and energy-band structure for the phenyl and the acene. We also examine the effect of disorder on the energies and the corresponding states.
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Adams, William Mark 1961. "APPLICATION OF THE VARIANCE-TO-MEAN RATIO METHOD FOR DETERMINING NEUTRON MULTIPLICATION PARAMETERS OF CRITICAL AND SUBCRITICAL REACTORS (REACTOR NOISE, FEYNMAN-ALPHA)." Thesis, The University of Arizona, 1985. http://hdl.handle.net/10150/275438.

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Books on the topic "Electronic noise – Mathematical models"

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institut, Moskovskiĭ ėnergeticheskiĭ. Shumovye i degradat︠s︡ionnye prot︠s︡essy v poluprovodnikovykh priborakh: Metrologii︠a︡, diagnostika, tekhnologii︠a︡, uchebnyĭ prot︠s︡ess : materialy dokladov Mezhdunarodnogo nauchno-metodicheskogo seminara, Moskva, 1-5 dekabri︠a︡ 2003 g. = Noise and degradation processes in semiconductor devices : metrology, diagnostic, technology, cirriculum [i.e., curriculum]. Moskva: Moskovskiĭ ėnerg. in-t (tekhn. universitet), 2004.

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Newman, M. E. J. Avalanches, scaling, and coherent noise. Ithaca, N.Y: Cornell Theory Center, Cornell University, 1996.

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Itō, Takatoshi. Intraday yen/dollar exchange rate movements: News or noise? Cambridge, MA (1050 Massachusetts Avenue, Cambridge, Mass. 02138): National Bureau of Economic Research, 1988.

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Williams, Noah. Small noise asymptotics for a stochastic growth model. Cambridge, Mass: National Bureau of Economic Research, 2003.

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Dow, James. Noise trading, delegated portfolio management, and economic welfare. Cambridge, MA: National Bureau of Economic Research, 1994.

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Williams, Noah. Small noise asymptotics for a stochastic growth model. Cambridge, MA: National Bureau of Economic Research, 2003.

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Marshall, Andrew. Mismatch and noise in modern IC processes. San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA): Morgan & Claypool Publishers, 2009.

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Bowlby, William. Predicting stop-and-go traffic noise levels. Washington, D.C: Transportation Research Board, National Research Council, 1989.

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Uosukainen, Seppo. JMC method applied to active control of sound: Theoretical extensions and new source configurations. Espoo [Finland]: Technical Research Centre of Finland, 1999.

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Christianus Bernardus Maria Te Stroet. Calibration of stochastic groundwater flow models: Estimation of noise statistics and model parameters. [Delft: Eburon], 1995.

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Book chapters on the topic "Electronic noise – Mathematical models"

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Fish, Peter J. "Noise Models." In Electronic Noise and Low Noise Design, 122–44. London: Macmillan Education UK, 1993. http://dx.doi.org/10.1007/978-1-349-23060-0_6.

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Demir, Alper, and Alberto Sangiovanni-Vincentelli. "Noise Models." In Analysis and Simulation of Noise in Nonlinear Electronic Circuits and Systems, 67–97. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4615-6063-0_3.

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Feng, Xiangchu, and Xiaolong Zhu. "Models for Multiplicative Noise Removal." In Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, 1–34. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-03009-4_60-1.

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Demir, Alper, and Alberto Sangiovanni-Vincentelli. "Mathematical Background." In Analysis and Simulation of Noise in Nonlinear Electronic Circuits and Systems, 5–65. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4615-6063-0_2.

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Munk, Axel, and Johannes Schmidt-Hieber. "Lower bounds for volatility estimation in microstructure noise models." In Institute of Mathematical Statistics Collections, 43–55. Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2010. http://dx.doi.org/10.1214/10-imscoll604.

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Pra, Paolo Dai, Giambattista Giacomin, and Daniele Regoli. "Noise-induced Periodicity: Some Stochastic Models for Complex Biological Systems." In Mathematical Models and Methods for Planet Earth, 25–35. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02657-2_3.

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Wellner, Jon A. "Gaussian white noise models: some results for monotone functions." In Institute of Mathematical Statistics Lecture Notes - Monograph Series, 87–104. Beachwood, OH: Institute of Mathematical Statistics, 2003. http://dx.doi.org/10.1214/lnms/1215092392.

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Zatuchny, Dmitry Alexandrovich, Ruslan Nikolaevich Akinshin, Nina Ivanovna Romancheva, Igor Viktorovich Avtin, and Yury Grigorievich Shatrakov. "Mathematical Models of Information Security in Civil Aircraft Flight-Navigation and Computing Systems." In Noise Resistance Enhancement in Aircraft Navigation and Connected Systems, 25–76. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0630-4_2.

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Musavishavazi, Seyedfakhredin, Mehrdad Mohannazadeh Bakhtiari, and Thomas Villmann. "A Mathematical Model for Optimum Error-Reject Trade-Off for Learning of Secure Classification Models in the Presence of Label Noise During Training." In Artificial Intelligence and Soft Computing, 547–54. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61401-0_51.

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García, Alejandro, Isaac Chairez, and Alexander Poznyak. "Identification and State Observation of Uncertain Chaotic Systems Using Projectional Differential Neural Networks." In Chaos Synchronization and Cryptography for Secure Communications, 42–67. IGI Global, 2011. http://dx.doi.org/10.4018/978-1-61520-737-4.ch003.

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The following chapter tackles the nonparametric identification and the state estimation for uncertain chaotic systems by the dynamic neural network approach. The developed algorithms consider the presence of additive noise in the state, for the case of identification, and in the measurable output, for the state estimation case. Mathematical model of the chaotic system is considered unknown, only the chaotic behavior as well as the maximal and minimal bound for each one of state variables are taking into account in the algorithm. Mathematical analysis and simulation results are presented. Application considering the so-called electronic Chua’s circuit is carried out; particularly a scheme of information encryption by the neural network observer with a noisy transmission is showed. Formal mathematical proofs and figures, illustrate the robustness of proposed algorithms mainly in the presence of noises with high magnitude.
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Conference papers on the topic "Electronic noise – Mathematical models"

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Bogdanov, Yu I., A. Yu Chernyavskiy, A. S. Holevo, V. F. Lukichev, and A. A. Orlikovsky. "Mathematical models of quantum noise." In International Conference on Micro-and Nano-Electronics 2012, edited by Alexander A. Orlikovsky. SPIE, 2013. http://dx.doi.org/10.1117/12.2017396.

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Avery, Seth M., and Robert D. Lorenz. "Measurement of Leadframe Strain in Electrically Active Power Semiconductors." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-50357.

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In this work, thermal-mechanical leadframe strain in an electrically active IGBT was measured using electronic speckle pattern interferometry (ESPI). ESPI is a non-contact optical technique capable of high resolution surface displacement measurements. The significant contribution of this paper is an experimental methodology by which strain can be measured in electrically active devices. A 3-D ESPI test stand was developed, combining two cameras to simultaneously capture the local (interconnect level) and global (device level) displacements. Through the combination of incremental sub-loads and mathematical recorrelation of speckle patterns, device power loads have been measured (which would have been otherwise impossible due to speckle decorrelation, which limits measurement of large deformations). A model-based tracking technique was developed from coupled experimental noise measurements and FE modeling — allowing for optimal strain solution to be extracted from noisy displacement results. The developed and experimentally-validated thermal-mechanical FE strain model agreed to within 7% of ESPI strain measurements.
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Батенков, Кирилл, Kirill Batenkov, Александр Миронов, Aleksandr Mironov, Михаил Стремоухов, Mihail Stremouhov, Кирилл Индюхов, and Kirill Indyuhov. "MATHEMATICAL REPRESENTATION OF IMPULSE NOISE IN XDSL COMMUNICATION SYSTEMS." In CAD/EDA/Simulation in Modern Electronics. Bryansk State Technical University, 2018. http://dx.doi.org/10.30987/conferencearticle_5c19e69c74a666.39267511.

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Faegh, Samira, Sohrab Eslami, and Nader Jalili. "An Adaptive Amplitude-Based Self-Sensing Piezoelectrically-Driven Microcantilever Sensor." In ASME 2010 Dynamic Systems and Control Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/dscc2010-4146.

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This paper presents an adaptive amplitude-based self-sensing strategy for ultrasmall tip mass estimation utilizing piezoelectrically-driven microcantilevers. The proposed configuration overcomes the inherent shortfalls (e.g., thermal drifts, electronic noise, and restriction to use in liquid media) currently exist in conventional systems. The microcantilever operates in self-sensing mode utilizing a piezoelectric patch deposited on the cantilever surface. The piezoelectric patch actuates the beam and at the same time senses the beam vibration through inverse and direct piezoelectric effects, respectively, which enables measurement of the surface induced stress. To remedy the measurement limitation at the microscale due to lack of sensitivity and temperature dependency of piezoelectric, an advanced auto-tunable self-sensing controller is proposed which balances the capacitance bridge network. Moreover, an optimization strategy is developed to minimize the error of the output voltage considering the fact that the individual time dependent coordinates are not measurable. Mathematical models and equations of motion are obtained using the Hamilton’s principle treating the microcantilever as a distributed-parameters system. Simulations are performed to demonstrate the effectiveness of the proposed technique.
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Tsegaye, Mikiyas S., Patrick E. Hopkins, Avik W. Ghosh, and Pamela M. Norris. "Calculating the Phonon Modes of Graphene Using the 4th Nearest Neighbor Force Constant Method." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-66726.

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Graphite has always been a very important material both industrially and academically due to its physical structure. But ever since the isolation of Graphene (a single sheet of Graphite) a few years ago, it’s been one of the most widely studied molecular systems for its potential applications in nano-electronics and other break-through areas. Some of the desirable traits of Graphene are its high thermal and electronic mobility, and its low noise properties. This paper outlines a standard method for calculating phonon dispersion curves in Graphene by making use of force constant measurements. This information is usually obtained from approximations of inter-atomic potentials, which involve derivatives of simplified potential approximations between every atom in Graphene to get the force constant tensors. In this paper, the measured values for the force constants are used in a mathematically rigorous way to calculate the Graphene phonon dispersion curves.
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Praefcke, Werner. "Robust and fast numerical color separation for mathematical printer models." In Electronic Imaging '99, edited by Giordano B. Beretta and Reiner Eschbach. SPIE, 1998. http://dx.doi.org/10.1117/12.334565.

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Phi, Cao Hung, Trinh Minh Hoang, and Tran Thanh Tung. "Analysis Noise Vibration of the Gearboxes using Mathematical Models." In the 10th International Conference. New York, New York, USA: ACM Press, 2018. http://dx.doi.org/10.1145/3177457.3177491.

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Cao, Hung-Phi. "Mathematical Models and the Noise -Vibration of the Gearboxes." In International Conference on Industrial Application Engineering 2015. The Institute of Industrial Applications Engineers, 2015. http://dx.doi.org/10.12792/iciae2015.102.

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Serykh, V. I., G. G. Egiazaryan, and Yu A. Palchun. "Analysis of Generalized Mathematical Models for QMS." In 2006 8th International Conference on Actual Problems of Electronic Instrument Engineering. IEEE, 2006. http://dx.doi.org/10.1109/apeie.2006.4292504.

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Singh, B. P., Meena Singh, Sanjay Kumar Roy, R. B. Patel, and B. P. Singh. "Mathematical Modeling of Electronic Devices and Circuits." In INTERNATIONAL CONFERENCE ON METHODS AND MODELS IN SCIENCE AND TECHNOLOGY (ICM2ST-10). AIP, 2010. http://dx.doi.org/10.1063/1.3526268.

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