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This monograph deals with approximation and noise cancellation of dynamical systems which include linear and nonlinear input/output relations. It will be of special interest to researchers, engineers and graduate students who have specialized in ?ltering theory and system theory. From noisy or noiseless data, reductionwillbemade.Anewmethodwhichreducesnoiseormodelsinformation will be proposed. Using this method will allow model description to be treated as noise reduction or model reduction. As proof of the e?cacy, this monograph provides new results and their extensions which can also be applied to nonlinear dynamical systems. To present the e?ectiveness of our method, many actual examples of noise and model information reduction will also be provided. Using the analysis of state space approach, the model reduction problem may have become a major theme of technology after 1966 for emphasizing e?ciency in the ?elds of control, economy, numerical analysis, and others. Noise reduction problems in the analysis of noisy dynamical systems may havebecomeamajorthemeoftechnologyafter1974foremphasizinge?ciencyin control.However,thesubjectsoftheseresearcheshavebeenmainlyconcentrated in linear systems. In common model reduction of linear systems in use today, a singular value decompositionofaHankelmatrixisusedto?ndareducedordermodel.However, the existence of the conditions of the reduced order model are derived without evaluationoftheresultantmodel.Inthecommontypicalnoisereductionoflinear systems in use today, the order and parameters of the systems are determined by minimizing information criterion. Approximate and noisy realization problems for input/output relations can be roughly stated as follows: A. The approximate realization problem. For any input/output map, ?nd one mathematical model such that it is similar totheinput/outputmapandhasalowerdimensionthanthegivenminimalstate spaceofadynamicalsystemwhichhasthesamebehaviortotheinput/outputmap. B. The noisy realization problem.

Discrete-time systems. --- Systems engineering. --- Control theory. --- Noise control. --- Systèmes échantillonnés --- Ingénierie des systèmes --- Théorie de la commande --- Bruit, lutte contre le --- Discrete-time systems --- Systems engineering --- Control theory --- Noise control --- Industrial & Management Engineering --- Operations Research --- Mechanical Engineering --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Noise prevention --- Engineering systems --- System engineering --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Design and construction --- Engineering. --- System theory. --- Statistical physics. --- Dynamical systems. --- Control engineering. --- Robotics. --- Mechatronics. --- Control, Robotics, Mechatronics. --- Systems Theory, Control. --- Statistical Physics, Dynamical Systems and Complexity. --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Machine theory --- Control engineering --- Control equipment --- Engineering instruments --- Programmable controllers --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical statistics --- Systems, Theory of --- Systems science --- Science --- Construction --- Industrial arts --- Technology --- Statistical methods --- Philosophy --- Complex Systems. --- Statistical Physics and Dynamical Systems. --- Systems theory. --- Dynamics --- Engineering --- Industrial engineering --- System analysis --- Digital control systems --- Discrete mathematics --- Linear time invariant systems

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This monograph deals with approximation and noise cancellation of dynamical systems which include linear and nonlinear input/output relationships. It also deal with approximation and noise cancellation of two dimensional arrays. It will be of special interest to researchers, engineers and graduate students who have specialized in filtering theory and system theory and digital images. This monograph is composed of two parts. Part I and Part II will deal with approximation and noise cancellation of dynamical systems or digital images respectively. From noiseless or noisy data, reduction will be made. A method which reduces model information or noise was proposed in the reference vol. 376 in LNCIS [Hasegawa, 2008]. Using this method will allow model description to be treated as noise reduction or model reduction without having to bother, for example, with solving many partial differential equations. This monograph will propose a new and easy method which produces the same results as the method treated in the reference. As proof of its advantageous effect, this monograph provides a new law in the sense of numerical experiments. The new and easy method is executed using the algebraic calculations without solving partial differential equations. For our purpose, many actual examples of model information and noise reduction will also be provided.

Discrete-time systems. --- Image processing. --- Noise control. --- Discrete-time systems --- Noise control --- Image processing --- Telecommunications --- Electrical Engineering --- Operations Research --- Applied Physics --- Civil & Environmental Engineering --- Electrical & Computer Engineering --- Engineering & Applied Sciences --- Systems engineering. --- Engineering systems --- System engineering --- Noise prevention --- Pictorial data processing --- Picture processing --- Processing, Image --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Design and construction --- Engineering. --- Computer vision. --- Control. --- Signal, Image and Speech Processing. --- Complexity. --- Control, Robotics, Mechatronics. --- Image Processing and Computer Vision. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Construction --- Industrial arts --- Technology --- Engineering --- Industrial engineering --- System analysis --- Acoustical engineering --- Environmental engineering --- Noise --- Imaging systems --- Optical data processing --- Digital control systems --- Linear time invariant systems --- Control and Systems Theory. --- Control engineering. --- Signal processing. --- Speech processing systems. --- Computational complexity. --- Robotics. --- Mechatronics. --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Machine theory --- Complexity, Computational --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Programmable controllers --- Optical equipment

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Applied physical engineering --- Engineering sciences. Technology --- Computer science --- procesautomatisering --- informatica --- systeemtheorie --- systeembeheer --- regeltechniek

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This monograph deals with control problems of discrete-time dynamical systems which include linear and nonlinear input/output relations. It will be of popular interest to researchers, engineers and graduate students who specialized in system theory. A new method which produces manipulated inputs is presented in the sense of state control and output control. This monograph provides new results and their extensions which can also be more applicable for nonlinear dynamical systems. To present the effectiveness of the method, many numerical examples of control problems are  provided as well.

Applied physical engineering --- Engineering sciences. Technology --- Artificial intelligence. Robotics. Simulation. Graphics --- systeemtheorie --- controleleer --- KI (kunstmatige intelligentie) --- systeembeheer --- ingenieurswetenschappen

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Thismonographisconcernedwithdescriptionanddesignfortwo-dimensional and three-dimensional images; it will be of special interest to researchers and graduate students who specialized in image processing and system theory. From the data in digital images, mathematical models will be constructed. Then new systems which describe faithfully any two-dimensional or thr- dimensional digital images will be proposed. Using the systems thus allows description to be treated as realization problem and design. By virtue of this approach, this monograph provides new results and their extensions which are designing of two-dimensional and three-dimensional images. Some actual design examples will be also shown. In usual image processing today, two-dimensional images are transformed into one-dimensional signals, then which are analyzed by means of various established methods in signal processing theory. Likewise, three-dimensional images are transformed into two-dimensional signals and these signals are analyzedbyestablishedmethodsintwo-dimensionalsignalprocessingtheory. Another common processing procedure employs tree structures such as qu- trees for two-dimensional images and oct-trees for three-dimensional ones.

Image processing --- Signal processing --- Three-dimensional imaging. --- Linear systems. --- Traitement d'images --- Traitement du signal --- Imagerie tridimensionnelle --- Systèmes linéaires --- Digital techniques. --- Techniques numériques --- Three-dimensional imaging --- Linear systems --- Applied Physics --- Engineering & Applied Sciences --- Digital techniques --- Digital signal processing --- Systems, Linear --- 3-D imaging --- 3D imaging --- Three-dimensional imaging systems --- Three-dimensional imaging techniques --- Three-dimensional visualization --- Visualization, Three-dimensional --- Digital image processing --- Engineering. --- Image processing. --- System theory. --- Control engineering. --- Robotics. --- Mechatronics. --- Control, Robotics, Mechatronics. --- Image Processing and Computer Vision. --- Systems Theory, Control. --- Differential equations, Linear --- System theory --- Imaging systems --- Digital communications --- Digital electronics --- Computer vision. --- Systems theory. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Programmable controllers --- Optical equipment