Download or read book The Generalized Complex Analytic Signal written by Edward Lawrence Pugh and published by . This book was released on 1970 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Complex and Hypercomplex Analytic Signals written by Stefan L. Hahn and published by Artech House. This book was released on 2016-12 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the bestselling Artech House classic title, Hilbert Transforms Signal Processing, this comprehensive new resource introduces complex and hypercomplex analytic signals and their applications. Professionals find in-depth explanations of the theory of multidimensional complex and hypercomplex signals illustrated with numerous examples and followed by practical applications. The survey of chosen hypercomplex algebras and the orthants of the n-dimensional Cartesian space and single-orthant operators are explored. This book also covers topics including, the polar representation of analytic signals, quasi-analytic signals, the space-frequency of n-D complex and hypercomplex signals as well as the causality of signals.
Download or read book Analytic Function Models of Noise and Modulation written by John H. Painter and published by . This book was released on 1969 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is essentially a presentation of the theory of complex analytic time functions applied to a representation of stochastic and deterministic time processes. By using analytic notation, noise and modulated signals are represented in the same manner. An intuitively satisfying, yet mathematically rigorous, method of transition from real to analytic processes is given. By use of the theory of distributions, the rotating vector, or phasor, method is generalized to arbitrary functions and stochastic processes. The advantages of analytic time function notation are exploited to derive correlation and spectral functions for both signal and noise processes. The polar and quadrature forms for band-pass processes are derived.
Download or read book Mathematics of the Discrete Fourier Transform DFT written by Julius O. Smith and published by Julius Smith. This book was released on 2008 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The DFT can be understood as a numerical approximation to the Fourier transform. However, the DFT has its own exact Fourier theory, and that is the focus of this book. The DFT is normally encountered as the Fast Fourier Transform (FFT)--a high-speed algorithm for computing the DFT. The FFT is used extensively in a wide range of digital signal processing applications, including spectrum analysis, high-speed convolution (linear filtering), filter banks, signal detection and estimation, system identification, audio compression (such as MPEG-II AAC), spectral modeling sound synthesis, and many others. In this book, certain topics in digital audio signal processing are introduced as example applications of the DFT"--Back cover
Download or read book The Weyl Operator and its Generalization written by Leon Cohen and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discovery of quantum mechanics in the years 1925-1930 necessitated the consideration of associating ordinary functions with non-commuting operators. Methods were proposed by Born/Jordan, Kirkwood, and Weyl. Sometime later, Moyal saw the connection between the Weyl rule and the Wigner distribution, which had been proposed by Wigner in 1932 as a way of doing quantum statistical mechanics. The basic idea of associating functions with operators has since been generalized and developed to a high degree. It has found several application fields, including quantum mechanics, pseudo-differential operators, time-frequency analysis, quantum optics, wave propagation, differential equations, image processing, radar, and sonar. This book aims at bringing together the results from the above mentioned fields in a unified manner and showing the reader how the methods have been applied. A wide audience is addressed, particularly students and researchers who want to obtain an up-to-date working knowledge of the field. The mathematics is accessible to the uninitiated reader and is presented in a straightforward manner.
Download or read book Statistical Signal Processing of Complex Valued Data written by Peter J. Schreier and published by Cambridge University Press. This book was released on 2010-02-04 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex-valued random signals are embedded in the very fabric of science and engineering, yet the usual assumptions made about their statistical behavior are often a poor representation of the underlying physics. This book deals with improper and noncircular complex signals, which do not conform to classical assumptions, and it demonstrates how correct treatment of these signals can have significant payoffs. The book begins with detailed coverage of the fundamental theory and presents a variety of tools and algorithms for dealing with improper and noncircular signals. It provides a comprehensive account of the main applications, covering detection, estimation, and signal analysis of stationary, nonstationary, and cyclostationary processes. Providing a systematic development from the origin of complex signals to their probabilistic description makes the theory accessible to newcomers. This book is ideal for graduate students and researchers working with complex data in a range of research areas from communications to oceanography.
Download or read book Quaternion Fourier Transforms for Signal and Image Processing written by Todd A. Ell and published by John Wiley & Sons. This book was released on 2014-06-02 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to Quaternion Fourier Transforms. QFT is a central component of processing color images and complex valued signals. The book’s attention to mathematical concepts, imaging applications, and Matlab compatibility render it an irreplaceable resource for students, scientists, researchers, and engineers.
Download or read book Speech Spectrum Analysis written by Sean A. Fulop and published by Springer Science & Business Media. This book was released on 2011-05-26 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The accurate determination of the speech spectrum, particularly for short frames, is commonly pursued in diverse areas including speech processing, recognition, and acoustic phonetics. With this book the author makes the subject of spectrum analysis understandable to a wide audience, including those with a solid background in general signal processing and those without such background. In keeping with these goals, this is not a book that replaces or attempts to cover the material found in a general signal processing textbook. Some essential signal processing concepts are presented in the first chapter, but even there the concepts are presented in a generally understandable fashion as far as is possible. Throughout the book, the focus is on applications to speech analysis; mathematical theory is provided for completeness, but these developments are set off in boxes for the benefit of those readers with sufficient background. Other readers may proceed through the main text, where the key results and applications will be presented in general heuristic terms, and illustrated with software routines and practical "show-and-tell" discussions of the results. At some points, the book refers to and uses the implementations in the Praat speech analysis software package, which has the advantages that it is used by many scientists around the world, and it is free and open source software. At other points, special software routines have been developed and made available to complement the book, and these are provided in the Matlab programming language. If the reader has the basic Matlab package, he/she will be able to immediately implement the programs in that platform---no extra "toolboxes" are required.
Download or read book Translational Recurrences written by Norbert Marwan and published by Springer. This book was released on 2014-08-27 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features 13 papers presented at the Fifth International Symposium on Recurrence Plots, held August 2013 in Chicago, IL. It examines recent applications and developments in recurrence plots and recurrence quantification analysis (RQA) with special emphasis on biological and cognitive systems and the analysis of coupled systems using cross-recurrence methods. Readers will discover new applications and insights into a range of systems provided by recurrence plot analysis and new theoretical and mathematical developments in recurrence plots. Recurrence plot based analysis is a powerful tool that operates on real-world complex systems that are nonlinear, non-stationary, noisy, of any statistical distribution, free of any particular model type and not particularly long. Quantitative analyses promote the detection of system state changes, synchronized dynamical regimes or classification of system states. The book will be of interest to an interdisciplinary audience of recurrence plot users and researchers interested in time series analysis of complex systems in general.
Download or read book Local Structure Tensor for Multidimensional Signal Processing written by Raúl San José Estépar and published by Presses univ. de Louvain. This book was released on 2007 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Feature extraction and, particularly, orientation estimation of multidimensional images is of paramount importance for the Image Processing and Computer Vision communities. This dissertation focuses on this topic; specifically, we deal with the problem of local structure tensor (LST) estimation, as a mean of characterizing the local behavior of a multidimensional signal. The LST can be seen as a measure of the uncertainty of a multidimensional signal with respect to a given orientation. LST estimation can be achieved by estimating the local energy of a signal in different orientations. Then, the LST is computed as a linear combination of the local energy for each orientation with a tensor basis whose elements are calculated for each orientation. This kind of methods for the estimation of the LST are based on quadrature filters to obtain the local energy of the signal. While the LST based on quadrature filters is well defined for signals that vary locally only in one orientation (simple signals), the estimation method fails with complex signals, i.e. signals that consist of several differently-oriented simple signals. In this dissertation, an analytical study of the distortions of the tensor eigenvalues due to such complex neighborhoods is carried out. From this analytical study, two constructive methods are proposed for the estimation of the LST. The first method is based on a maximum likelihood estimation of the quadrature filter outputs. The second method uses a measure of phase consistency based on generalized quadrature filters which are formally derived from an extension of the analytic signal to multidimensional signals known as the monogenic signal. The interpretation of a multidimensional image as a function graph, i.e. a Riemannian manifold, instead of just intensity variations on the Euclidean space, has important implications that are exploited in this dissertation. Image processing tasks can then be performed by solving partial differential equations on the Riemannian manifold. In this dissertation, Riemannian geometry is used to study the evolution of fronts under mean curvature flow on a Riemannian manifold using a level set framework. For our purposes, the Riemannian manifold is defined by the induced metric of the image that is related to the LST. The Riemannian mean curvature flow is the theoretical basis for the definition of a level set segmentation method. The methods proposed in this dissertation are applied to two medical image applications. The first consists in a freehand 3D ultrasound reconstruction technique that uses the LST to perform an adaptive interpolation based on normalized convolution. Our results show that our method outperforms traditional technique for this interpolation problem. The second application uses the level set method based on Riemannian mean curvature flow to segment anatomical structures in dataset from magnetic resonance imaging (MRI), computed tomography (CT) and ultrasound (US). This novel method reveals as a feasible approach to medical image segmentation.
Download or read book Stochastic Processes in Physics Chemistry and Biology written by Jan A. Freund and published by Springer. This book was released on 2008-01-11 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of stochastic processes originally grew out of efforts to describe Brownian motion quantitatively. Today it provides a huge arsenal of methods suitable for analyzing the influence of noise on a wide range of systems. The credit for acquiring all the deep insights and powerful methods is due ma- ly to a handful of physicists and mathematicians: Einstein, Smoluchowski, Langevin, Wiener, Stratonovich, etc. Hence it is no surprise that until - cently the bulk of basic and applied stochastic research was devoted to purely mathematical and physical questions. However, in the last decade we have witnessed an enormous growth of results achieved in other sciences - especially chemistry and biology - based on applying methods of stochastic processes. One reason for this stochastics boom may be that the realization that noise plays a constructive rather than the expected deteriorating role has spread to communities beyond physics. Besides their aesthetic appeal these noise-induced, noise-supported or noise-enhanced effects sometimes offer an explanation for so far open pr- lems (information transmission in the nervous system and information p- cessing in the brain, processes at the cell level, enzymatic reactions, etc.). They may also pave the way to novel technological applications (noise-- hanced reaction rates, noise-induced transport and separation on the na- scale, etc.). Key words to be mentioned in this context are stochastic r- onance, Brownian motors or ratchets, and noise-supported phenomena in excitable systems.
Download or read book General Theory of Light Propagation and Imaging Through the Atmosphere written by T. Stewart McKechnie and published by Springer Nature. This book was released on 2022-10-06 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2nd edition lays out an updated version of the general theory of light propagation and imaging through Earth’s turbulent atmosphere initially developed in the late ‘70s and ‘80s, with additional applications in the areas of laser communications and high-energy laser beam propagation. New material includes a chapter providing a comprehensive mathematical tool set for precisely characterizing image formation with the anticipated Extremely Large Telescopes (ELTS), enabling a staggering range of star image shapes and sizes; existing chapters rewritten or modified so as to supplement the mathematics with clearer physical insight through written and graphical means; a history of the development of present-day understanding of light propagation and imaging through the atmosphere as represented by the general theory described. Beginning with the rudimentary, geometrical-optics based understanding of a century ago, it describes advances made in the 1960s, including the development of the ‘Kolmogorov theory,’ the deficiencies of which undermined its credibility, but not before it had done enormous damage, such as construction of a generation of underperforming ‘light bucket’ telescopes. The general theory requires no a priori turbulence assumptions. Instead, it provides means for calculating the turbulence properties directly from readily-measurable properties of star images.
Download or read book Hypercomplex Analysis New Perspectives and Applications written by Swanhild Bernstein and published by Springer. This book was released on 2014-10-10 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function. In recent decades this theory has come to the forefront of higher dimensional analysis. There are several approaches to this: quaternionic analysis which merely uses quaternions, Clifford analysis which relies on Clifford algebras, and generalizations of complex variables to higher dimensions such as split-complex variables. This book includes a selection of papers presented at the session on quaternionic and hypercomplex analysis at the ISAAC conference 2013 in Krakow, Poland. The topics covered represent new perspectives and current trends in hypercomplex analysis and applications to mathematical physics, image analysis and processing, and mechanics.
Download or read book Handbook of Radar Signal Analysis written by Bassem R. Mahafza and published by CRC Press. This book was released on 2021-08-30 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new handbook on radar signal analysis adopts a deliberate and systematic approach. It uses a clear and consistent level of delivery while maintaining strong and easy-to-follow mathematical details. The emphasis of this book is on radar signal types and their relevant signal processing and not on radar systems hardware or components. This handbook serves as a valuable reference to a wide range of audience. More specifically, college-level students, practicing radar engineers, as well as casual readers of the subject are the intended target audience of the first few chapters of this book. As the book chapters progress, these grow in complexity and specificity. Accordingly, later chapters are intended for practicing engineers, graduate college students, and advanced readers. Finally, the last few chapters contain several special topics on radar systems that are both educational and scientifically entertaining to all readers. The presentation of topics in this handbook takes the reader on a scientific journey whose major landmarks comprise the different radar subsystems and components. In this context, the chapters follow the radar signal along this journey from its birth to the end of its life. Along the way, the different relevant radar subsystems are analyzed and discussed in great detail. The chapter contributors of this new handbook comprise experienced academia members and practicing radar engineers. Their combined years of academic and real-world experiences are in excess of 175. Together, they bring a unique, easy-to-follow mix of mathematical and practical presentations of the topics discussed in this book. See the "Chapter Contributors" section to learn more about these individuals.
Download or read book Wireless Transceiver Architecture written by Pierre Baudin and published by John Wiley & Sons. This book was released on 2014-12-15 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fully comprehensive reference combining digital communications and RFIC (Radio Frequency Integrated Circuits) in one complete volume There are many books which focus on the physical implementation of the RF/analog part of transceivers, such as the CMOS design, or the signal processing involved in digital communications. However, there is little material dedicated to transceiver architecture and system design. Similarly, much of the existing literature looks at concepts useful for dimensioning, yet offers little practical information on how to proceed for dimensioning a line-up from scratch, and on the reasons for proceeding that way. This book redresses the balance by explaining the architecture of transceivers and their dimensioning from the perspective of a RFIC architect from within industry. It bridges the gap between digital communication systems and radiofrequency integrated circuit design, covering wireless transceiver architecture and system design from both system level and circuit designer aspects. • Covers digital communication theory, electromagnetism theory and wireless networks organization, from theories to implementation, for deriving the minimum set of constraints to be fulfilled by transceivers • Details the limitations in the physical implementation of transceivers to be considered for their dimensioning, in terms of noise, nonlinearity, and RF impairments • Presents transceiver architecture and system design in terms of transceivers budgets, transceivers architectures, and algorithms for transceivers
Download or read book Continuous Time Signals written by Yuriy Shmaliy and published by Springer Science & Business Media. This book was released on 2006-10-04 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an extended description of continuous-time signals related to signals and systems. As a time-varying process of any physical state of any object, which serves for representation, detection, and transmission of messages, a modern electrical signal possesses, in applications, many specific properties. The text covers principle foundations of signals theory. Presenting bandlimited and analytic signals, the book reviews the methods of their description, transformation (by Hilbert transform), and sampling.
Download or read book Signal Analysis written by Ronald L. Allen and published by John Wiley & Sons. This book was released on 2004-06-07 with total page 961 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a well-rounded, mathematical approach to problems in signal interpretation using the latest time, frequency, and mixed-domain methods Equally useful as a reference, an up-to-date review, a learning tool, and a resource for signal analysis techniques Provides a gradual introduction to the mathematics so that the less mathematically adept reader will not be overwhelmed with instant hard analysis Covers Hilbert spaces, complex analysis, distributions, random signals, analog Fourier transforms, and more
