discrete stochastic processes and optimal filtering

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Discrete Stochastic Processes And Optimal Filtering

Author : Jean-Claude Bertein
ISBN : 9781118615492
Genre : Technology & Engineering
File Size : 47. 72 MB
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Optimal filtering applied to stationary and non-stationary signals provides the most efficient means of dealing with problems arising from the extraction of noise signals. Moreover, it is a fundamental feature in a range of applications, such as in navigation in aerospace and aeronautics, filter processing in the telecommunications industry, etc. This book provides a comprehensive overview of this area, discussing random and Gaussian vectors, outlining the results necessary for the creation of Wiener and adaptive filters used for stationary signals, as well as examining Kalman filters which are used in relation to non-stationary signals. Exercises with solutions feature in each chapter to demonstrate the practical application of these ideas using Matlab.

Optimal Filtering

Author : V.N. Fomin
ISBN : 9789401146913
Genre : Mathematics
File Size : 32. 94 MB
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In this volume the investigations of filtering problems, a start on which has been made in [55], are being continued and are devoted to theoretical problems of processing stochastic fields. The derivation of the theory of processing stochastic fields is similar to that of the theory extensively developed for stochastic processes ('stochastic fields with a one-dimensional domain'). Nevertheless there exist essential distinctions between these cases making a construction of the theory for the multi-dimensional case in such a way difficult. Among these are the absence of the notion of the 'past-future' in the case of fields, which plays a fundamental role in constructing stochastic processes theory. So attempts to introduce naturally the notion of the causality (non-anticipativity) when synthesising stable filters designed for processing fields have not met with success. Mathematically, principal distinctions between multi-dimensional and one-dimensional cases imply that the set of roots of a multi-variable polyno mial does not necessary consist of a finite number of isolated points. From the main theorem of algebra it follows that in the one-dimensional case every poly nomial of degree n has just n roots (considering their multiplicity) in the com plex plane. As a consequence, in particular, an arbitrary rational function ¢(.

Stochastic Processes And Filtering Theory

Author : Andrew H. Jazwinski
ISBN : 9780486318196
Genre : Science
File Size : 56. 11 MB
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This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well. Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probability theory and stochastic processes, the author introduces and defines the problems of filtering, prediction, and smoothing. He presents the mathematical solutions to nonlinear filtering problems, and he specializes the nonlinear theory to linear problems. The final chapters deal with applications, addressing the development of approximate nonlinear filters, and presenting a critical analysis of their performance.

Studies In Optimum Filtering Of Single And Multiple Stochastic Processes

Author : Stephen Milton Simpson
ISBN : OCLC:14918049
Genre : Digital filters (Mathematics)
File Size : 74. 31 MB
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This report treats the design of discrete filters for the detection of signals caused by nuclear explosions on digitized seismic recordings. The theoretical aspects of filter design are treated, together with the setting up of the necessary formulas for realizing the filters on digital computers. Recursive computational schemes are presented for normal equations of Toeplitz form. For single processes the Levinson recursion for the extension of the prediction error operator and the extension of the general filter is developed, as well as the recursion to move the output origin. A corresponding development is given for multi-channel processes, as well as a development of the recursion to larger operators for the multi-dimensional processes. The prediction problem for single stationary time series is reviewed and the least square and Kolmogoroff solutions given. Extension is then made to the multiple case, the least squares equations set up and the Wiener-Masani factorization described. Heuristic use is made of the Hilbert space property of time series. A digital computer program for performing the Wiener-Masani factorization is discussed. (Author).

Stochastic Processes Estimation And Control

Author : Jason L. Speyer
ISBN : 9780898718591
Genre : Control theory
File Size : 23. 41 MB
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Uncertainty and risk are integral to engineering because real systems have inherent ambiguities that arise naturally or due to our inability to model complex physics. The authors discuss probability theory, stochastic processes, estimation, and stochastic control strategies and show how probability can be used to model uncertainty in control and estimation problems. The material is practical and rich in research opportunities.

Introduction To Random Signals And Noise

Author : Wim C. Van Etten
ISBN : 9780470024126
Genre : Science
File Size : 30. 64 MB
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Random signals and noise are present in many engineering systems and networks. Signal processing techniques allow engineers to distinguish between useful signals in audio, video or communication equipment, and interference, which disturbs the desired signal. With a strong mathematical grounding, this text provides a clear introduction to the fundamentals of stochastic processes and their practical applications to random signals and noise. With worked examples, problems, and detailed appendices, Introduction to Random Signals and Noise gives the reader the knowledge to design optimum systems for effectively coping with unwanted signals. Key features: Considers a wide range of signals and noise, including analogue, discrete-time and bandpass signals in both time and frequency domains. Analyses the basics of digital signal detection using matched filtering, signal space representation and correlation receiver. Examines optimal filtering methods and their consequences. Presents a detailed discussion of the topic of Poisson processes and shot noise. An excellent resource for professional engineers developing communication systems, semiconductor devices, and audio and video equipment, this book is also ideal for senior undergraduate and graduate students in Electronic and Electrical Engineering.

Discrete Time Stochastic Systems

Author : Torsten Söderström
ISBN : 9781447101017
Genre : Mathematics
File Size : 85. 19 MB
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This comprehensive introduction to the estimation and control of dynamic stochastic systems provides complete derivations of key results. The second edition includes improved and updated material, and a new presentation of polynomial control and new derivation of linear-quadratic-Gaussian control.

Nonlinear Filtering And Optimal Phase Tracking

Author : Zeev Schuss
ISBN : 1461404878
Genre : Mathematics
File Size : 25. 30 MB
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This book offers an analytical rather than measure-theoretical approach to the derivation of the partial differential equations of nonlinear filtering theory. The basis for this approach is the discrete numerical scheme used in Monte-Carlo simulations of stochastic differential equations and Wiener's associated path integral representation of the transition probability density. Furthermore, it presents analytical methods for constructing asymptotic approximations to their solution and for synthesizing asymptotically optimal filters. It also offers a new approach to the phase tracking problem, based on optimizing the mean time to loss of lock. The book is based on lecture notes from a one-semester special topics course on stochastic processes and their applications that the author taught many times to graduate students of mathematics, applied mathematics, physics, chemistry, computer science, electrical engineering, and other disciplines. The book contains exercises and worked-out examples aimed at illustrating the methods of mathematical modeling and performance analysis of phase trackers.

Adaptive Filtering Prediction And Control

Author : Graham C Goodwin
ISBN : 9780486137728
Genre : Technology & Engineering
File Size : 26. 21 MB
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This unified survey focuses on linear discrete-time systems and explores natural extensions to nonlinear systems. It emphasizes discrete-time systems, summarizing theoretical and practical aspects of a large class of adaptive algorithms. 1984 edition.

Optimal Filtering

Author : Brian D. O. Anderson
ISBN : 9780486136899
Genre : Science
File Size : 78. 48 MB
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Graduate-level text extends studies of signal processing, particularly regarding communication systems and digital filtering theory. Topics include filtering, linear systems, and estimation; discrete-time Kalman filter; time-invariant filters; more. 1979 edition.

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