Statistical signal processing

This volume describes the essential tools and techniques of statistical signal processing. At every stage, theoretical ideas are linked to specific applications in communications and signal processing. The book begins with an overview of basic probability, random objects, expectation, and secondorder moment theory, followed by a wide variety of examples of the most popular random process models and their basic uses and properties.
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The main thrust is to provide students with a solid understanding of a number of important and related advanced topics in digital signal processing such as Wiener filters, power spectrum estimation, signal modeling and adaptive filtering. Scores of worked examples illustrate fine points, compare techniques and algorithms and facilitate comprehension of fundamental concepts. Also features an abundance of interesting and challenging problems at the end of every chapter.
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Recent advances in genomic studies have stimulated synergetic research and development in many crossdisciplinary areas. Genomic data, especially the recent largescale microarray gene expression data, represents enormous challenges for signal processing and statistics in processing these vast data to reveal the complex biological functionality. This perspective naturally leads to a new field, genomic signal processing (GSP)
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Much of modern digital signal processing is concernedwith the extraction of information fromsignals whichare noisy, orwhichbehave randomlywhile still revealingsomeattributeor parameterof a system or environment under observation. The term in popular use now for this kind of computation is statistical signal processing, and much of this Handbook is devoted to this very subject. Statistical signal processing is classical statistical inference applied to problems of interest to electrical engineers, with the added twist that answers are often required in “real time”, perhaps seconds or less.
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Processes encountered in statistical signal processing, communications, and time series analysis applications are often assumed stationary. The plethora of available
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MONSON H. HAYES is a Professor of Electrical and Computer Engineering at the Georgia Institute of Technology in Atlanta, Georgia. He received his B.A. degree in Physics from the University of California, Berkeley, and his M.S.E.E. and Sc.D. degrees in Electrical Engineering and Computer Science from M.I.T. His research interests are in digital signal processing with applications in image and video processing.
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The origins of this book lie in our earlier book Random Processes: A Mathematical Approach for Engineers, Prentice Hall, 1986. This book began as a second edition to the earlier book and the basic goal remains unchanged  to introduce the fundamental ideas and mechanics of random processes to engineers in a way that accurately reects the underlying mathematics, but does not require an extensive mathematical background and does not belabor detailed general proofs when simple cases suce to get the basic ideas across....
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The origins of this book lie in our earlier book Random Processes: A Mathematical Approach for Engineers, Prentice Hall, 1986. This book began as a second edition to the earlier book and the basic goal remains unchanged — to introduce the fundamental ideas and mechanics of random processes to engineers in a way that accurately reflects the underlying mathematics, but does not require an extensive mathematical background and does not belabor detailed general proofs when simple cases suffice to get the basic ideas across.......
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Detection and classification arise in signal processing problems whenever a decision is to be made among a finite number of hypotheses concerning an observed waveform. Signal detection algorithms decide whether the waveform consists of “noise alone” or “signal masked by noise.” Signal classification algorithms decide whether a detected signal belongs to one or another of prespecified classes of signals. The objective of signal detection and classification theory is to specify systematic strategies for designing algorithms which minimize the average number of decision errors.
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The past 20 years witnessed an expansion of power spectrum estimation techniques, which have proved essential in many applications, such as communications, sonar, radar, speech/image processing, geophysics, and biomedical signal processing [13, 11, 7]. In power spectrum estimation the process under consideration is treated as a superposition of statistically uncorrelated harmonic components. The distribution of power among these frequency components is the power spectrum. As such, phase relations between frequency components are suppressed....
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Processes encountered in statistical signal processing, communications, and time series analysis applications are often assumed stationary.
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EURASIP Journal on Applied Signal Processing 2003:3, 223–237 c 2003 Hindawi Publishing Corporation Removing Impulse Bursts from Images by TrainingBased Filtering Pertti Koivisto Department of Mathematics, Statistics, and Philosophy, University of Tampere, Finland Institute of Signal Processing, Tampere University of Technology, Tampere, Finland Email: pertti.koivisto@tut.ﬁ Jaakko Astola Institute of Signal Processing, Tampere University of Technology, Tampere, Finland Email: jaakko.astola@tut.
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EURASIP Journal on Applied Signal Processing 2003:5, 449–460 c 2003 Hindawi Publishing Corporation Multilevel Wavelet Feature Statistics for Efﬁcient Retrieval, Transmission, and Display of Medical Images by Hybrid Encoding Shuyu Yang Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, TX 794093102, USA Email: shu.yang@ttu.edu Sunanda Mitra Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, TX 794093102, USA Email: sunanda.mitra@coe.ttu.
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Beamforming is a signal processing technique. It has been studied in many areas such as radar, sonar, seismology and wireless communications, to name but a few. It can be used for a myriad of purposes, such as detecting the presence of a signal, estimating the direction of arrival, and enhancing a desired signal from its measurements corrupted by noise, competing sources and reverberation. Actually, Beamforming has been adopted by the audio research society, mostly to separate or extract speech for noisy environment.
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Characterizing the Performance of Adaptive Filters 19.3 Analytical Models, Assumptions, and Deﬁnitions System Identiﬁcation Model for the Desired Response Signal • Statistical Models for the Input Signal • The Independence Assumptions • Useful Deﬁnitions 19.4 Analysis of the LMS Adaptive Filter Mean Analysis • MeanSquare Analysis 19.5 Performance Issues Basic Criteria for Performance • Identifying Stationary Systems • Tracking TimeVarying Systems Normalized Step Sizes • Adaptive and Matrix Step Sizes • Other TimeVarying Step Size Methods 19.
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The focus of this chapter is on inverse problems—what they are, where they manifest themselves in the realmof digital signal processing (DSP), and how they might be “solved1.”
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Genetic Algorithms K.F. Man, K.S. Tang and S. Kwong Neural Networks for Modelling and Control of Dynamic Systems M. Nørgaard, O. Ravn, L.K. Hansen and N.K. Poulsen Modelling and Control of Robot Manipulators (2nd Edition) L. Sciavicco and B. Siciliano Fault Detection and Diagnosis in Industrial Systems L.H. Chiang, E.L. Russell and R.D. Braatz Soft Computing L. Fortuna, G. Rizzotto, M. Lavorgna, G. Nunnari, M.G. Xibilia and R. Caponetto Statistical Signal Processing T. Chonavel Discretetime Stochastic Processes (2nd Edition) T. Söderström Parallel...
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Recursive LeastSquares Adaptive Filters Array Algorithms Elementary Circular Rotations • Elementary Hyperbolic Rotations • SquareRootFree and Householder Transformations • A Numerical Example Geometric Interpretation • Statistical Interpretation Geometric Interpretation • Statistical Interpretation Reducing to the Regularized Form • Time Updates Estimation Errors and the Conversion Factor • Update of the Minimum Cost Motivation • A Very Useful Lemma • The Inverse QR Algorithm • The QR Algorithm The Prewindowed Case • LowRank Property • A Fast Array Algorithm • The Fast Transversal Filte...
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This raw curve can be converted into the complete Gaussian by adding an adjustable mean, µ, and standard deviation, F. In addition, the equation must be normalized so that the total area under the curve is equal to one, a requirement of all probability distribution functions. This results in the general form of the normal distribution, one of the most important relations in statistics and probability: EQUATION 28 Equation for the normal distribution, also called the Gauss distribution, or simply a Gaussian.
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Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2011, Article ID 980805, 15 pages doi:10.1155/2011/980805 Research Article Optimal Multitaper Wigner Spectrum Estimation of a Class of Locally Stationary Processes Using Hermite Functions Maria HanssonSandsten (EURASIP Member) Mathematical Statistics, Centre for Mathematical Sciences, Lund University, P.O. Box 118, 221 00 Lund, Sweden Correspondence should be addressed to Maria HanssonSandsten, sandsten@maths.lth.
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