complex-valued-matrix-derivatives

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In this complete introduction to the theory of finding derivatives of scalar-, vector- and matrix-valued functions with respect to complex matrix variables, Hjørungnes describes an essential set of mathematical tools for solving research problems where unknown parameters are contained in complex-valued matrices. The first book examining complex-valued matrix derivatives from an engineering perspective, it uses numerous practical examples from signal processing and communications to demonstrate how these tools can be used to analyze and optimize the performance of engineering systems. Covering un-patterned and certain patterned matrices, this self-contained and easy-to-follow reference deals with applications in a range of areas including wireless communications, control theory, adaptive filtering, resource management and digital signal processing. Over 80 end-of-chapter exercises are provided, with a complete solutions manual available online.

Recent advancements in signal processing and computerised methods are expected to underpin the future progress of biomedical research and technology, particularly in measuring and assessing signals and images from the human body. This book focuses on singular spectrum analysis (SSA), an effective approach for single channel signal analysis, and its bivariate, multivariate, tensor based, complex-valued, quaternion-valued and robust variants. SSA currently has numerous applications in detecting abnormalities in quasi-periodic biosignals, such as electrocardiograms, (ECGs or EKGs), oxygen levels, arterial pressure, and electroencephalograms (EEGs). Singular Spectrum Analysis of Biomedical Signals presents relatively newly applied concepts for biomedical applications of SSA, including: Signal source separation, extraction, decomposition, and factorization Physiological, biological, and biochemical signal processing A new SSA grouping algorithm for filtering and noise reduction of genetics data Prediction of various clinical events The book introduces a new mathematical and signal processing technique for the decomposition of widely available single channel biomedical data. It also provides illustrations of new signal processing results in the form of signals, graphs, images, and tables to reinforce understanding of the related concepts. Singular Spectrum Analysis of Biomedical Signals enhances current clinical knowledge and aids physicians in improving diagnosis, treatment and monitoring some clinical abnormalities. It also lays groundwork for progress in SSA by making suggestions for future research.

Leading experts present the latest research results in adaptive signal processing Recent developments in signal processing have made it clear that significant performance gains can be achieved beyond those achievable using standard adaptive filtering approaches. Adaptive Signal Processing presents the next generation of algorithms that will produce these desired results, with an emphasis on important applications and theoretical advancements. This highly unique resource brings together leading authorities in the field writing on the key topics of significance, each at the cutting edge of its own area of specialty. It begins by addressing the problem of optimization in the complex domain, fully developing a framework that enables taking full advantage of the power of complex-valued processing. Then, the challenges of multichannel processing of complex-valued signals are explored. This comprehensive volume goes on to cover Turbo processing, tracking in the subspace domain, nonlinear sequential state estimation, and speech-bandwidth extension. Examines the seven most important topics in adaptive filtering that will define the next-generation adaptive filtering solutions Introduces the powerful adaptive signal processing methods developed within the last ten years to account for the characteristics of real-life data: non-Gaussianity, non-circularity, non-stationarity, and non-linearity Features self-contained chapters, numerous examples to clarify concepts, and end-of-chapter problems to reinforce understanding of the material Contains contributions from acknowledged leaders in the field Adaptive Signal Processing is an invaluable tool for graduate students, researchers, and practitioners working in the areas of signal processing, communications, controls, radar, sonar, and biomedical engineering.

This book was written in response to the growing demand for a text that provides a unified treatment of linear and nonlinear complex valued adaptive filters, and methods for the processing of general complex signals (circular and noncircular). It brings together adaptive filtering algorithms for feedforward (transversal) and feedback architectures and the recent developments in the statistics of complex variable, under the powerful frameworks of CR (Wirtinger) calculus and augmented complex statistics. This offers a number of theoretical performance gains, which is illustrated on both stochastic gradient algorithms, such as the augmented complex least mean square (ACLMS), and those based on Kalman filters. This work is supported by a number of simulations using synthetic and real world data, including the noncircular and intermittent radar and wind signals.

Unique in addressing two different problems – soundvisualization and manipulation – in a unified way Advances in signal processing technology are enabling ever moreaccurate visualization of existing sound fields and preciselydefined sound field production. The idea of explaining both theproblem of sound visualization and the problem of the manipulationof sound within one book supports this inter-related area ofstudy. With rapid development of array technologies, it ispossible to do much in terms of visualization and manipulation,among other technologies involved with the spatial distribution ofsound. This book aims to explore various basic functions for thevisualization and manipulation and demonstrate to the reader howthese properties determine the quality of visualization andmanipulation. The first half of the book introduces some basic andgeneral concepts and theories and the second part of the bookexplains a number of techniques in sound visualization andmanipulation. It offers a unified presentation to two verydifferent topics - sound field visualization techniques based onmicrophone arrays, and techniques for generation of controlledsound fields using loudspeaker arrays. The authors emphasize thesimilarities between these two physical problems and between themathematical methods used for solving them. With extensive examples throughout the book, chapters include:Acoustic Wave Equation and its Basic Physical Measures, AcousticWave Equation and its Basic Physical Measures, Basic Theory ofSound Visualization, Acoustic Holography, Beamforming, Basic Theoryof Sound Manipulation, Sound Focusing, and Sound FieldReproduction. The first book to combine both the visualization andmanipulation of sound technologies in one comprehensive volume Presents the basic concepts using simple one dimensional casesand then extends the concept to three dimensional cases, enablingeasier understanding of the fundamental concepts through the use ofminimum mathematics Provides a solid understanding of associated physics as well asmathematical concepts for understanding the technologies,addressing diffraction problems in an integrated format by usingKirchhoff-Helmholtz integral equation Uses extensive examples demonstrating the benefits anddrawbacks of various applications, including beamforming andacoustic holography A valuable resource forpost/graduate students, acousticengineers, audio and noise control system developers

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.

Vols. 11 and 13 includes the Proceedings of the 2nd, 3rd, International Symposium on Geophysical Theory and Computers, Rehovoth, Israel, etc., 1965-66.

This book deals with a wide class of novel and efficient adaptive signal processing techniques developed to restore signals from noisy and degraded observations. These signals include those acquired from still or video cameras, electron microscopes, radar, X-rays, or ultrasound devices, and are used for various purposes, including entertainment, medical, business, industrial, military, civil, security, and scientific. In many cases useful information and high quality must be extracted from the imaging. However, often raw signals are not directly suitable for this purpose and must be processed in some way. Such processing is called signal reconstruction. This book is devoted to a recent and original approach to signal reconstruction based on combining two independent ideas: local polynomial approximation and the intersection of confidence interval rule.

This book develops the mathematical theory of linear adaptive filters with finite impulse response. Examples and computer experiment applications illustrate the theory and principles. The second edition has also been restructured with an introduction followed by four parts: discrete-time wide-sense station stochastic process; linear optimum filtering; linear FIR adaptive filtering; limitations, extensions and discussions. on blind deconvolution, new appendix material on complex variables and regulation.

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