The requirement of causality in system theory is inevitably accompanied by the appearance of certain mathematical operations, namely the Riesz proj- tion,theHilberttransform,andthespectralfactorizationmapping.Aclassical exampleillustratingthisisthedeterminationoftheso-calledWiener?lter(the linear, minimum means square error estimation ?lter for stationary stochastic sequences [88]). If the ?lter is not required to be causal, the transfer function of the Wiener ?lter is simply given by H(?)=? (?)/? (?),where ? (?) xy xx xx and ? (?) are certain given functions. However, if one requires that the - xy timation ?lter is causal, the transfer function of the optimal ?lter is given by 1 ? (?) xy H(?)= P ,?? (??,?] . + [? ] (?) [? ] (?) xx + xx? Here [? ] and [? ] represent the so called spectral factors of ? ,and xx + xx? xx P is the so called Riesz projection. Thus, compared to the non-causal ?lter, + two additional operations are necessary for the determination of the causal ?lter, namely the spectral factorization mapping ? ? ([? ] ,[? ] ),and xx xx + xx? the Riesz projection P .

Concisely covers all the important concepts in an easy-to-understand way Gaining a strong sense of signals and systems fundamentals is key for general proficiency in any electronic engineering discipline, and critical for specialists in signal processing, communication, and control. At the same time, there is a pressing need to gain mastery of these concepts quickly, and in a manner that will be immediately applicable in the real word. Simultaneous study of both continuous and discrete signals and systems presents a much easy path to understanding signals and systems analysis. In A Practical Approach to Signals and Systems, Sundararajan details the discrete version first followed by the corresponding continuous version for each topic, as discrete signals and systems are more often used in practice and their concepts are relatively easier to understand. In addition to examples of typical applications of analysis methods, the author gives comprehensive coverage of transform methods, emphasizing practical methods of analysis and physical interpretations of concepts. Gives equal emphasis to theory and practice Presents methods that can be immediately applied Complete treatment of transform methods Expanded coverage of Fourier analysis Self-contained: starts from the basics and discusses applications Visual aids and examples makes the subject easier to understand End-of-chapter exercises, with a extensive solutions manual for instructors MATLAB software for readers to download and practice on their own Presentation slides with book figures and slides with lecture notes A Practical Approach to Signals and Systems is an excellent resource for the electrical engineering student or professional to quickly gain an understanding of signal analysis concepts - concepts which all electrical engineers will eventually encounter no matter what their specialization. For aspiring engineers in signal processing, communication, and control, the topics presented will form a sound foundation to their future study, while allowing them to quickly move on to more advanced topics in the area. Scientists in chemical, mechanical, and biomedical areas will also benefit from this book, as increasing overlap with electrical engineering solutions and applications will require a working understanding of signals. Compact and self contained, A Practical Approach to Signals and Systems be used for courses or self-study, or as a reference book.

"Signal Processing and Systems Theory" is concerned with the study of H-optimization for digital signal processing and discrete-time control systems. The first three chapters present the basic theory and standard methods in digital filtering and systems from the frequency-domain approach, followed by a discussion of the general theory of approximation in Hardy spaces. AAK theory is introduced, first for finite-rank operators and then more generally, before being extended to the multi-input/multi-output setting. This mathematically rigorous book is self-contained and suitable for self-study. The advanced mathematical results derived here are applicable to digital control systems and digital filtering.

This book attempts to improve algorithms by novel theories and complex data analysis in different scopes including object detection, remote sensing, data transmission, data fusion, gesture recognition, and medical image processing and analysis. The book is directed to the Ph.D. students, professors, researchers, and software developers working in the areas of digital video processing and computer vision technologies.

Exploring signals and systems, this work develops continuous-time and discrete-time concepts, highlighting the differences and similarities. Two chapters deal with the Laplace transform and the Z-transform. Basic methods such as filtering, communication an

This is volume 1 of a 2 volume set. This volume focuses on "channel estimation and equalization."

Discover the Applicability, Benefits, and Potential of New Technologies As advances in algorithms and computer technology have bolstered the digital signal processing capabilities of real-time sonar, radar, and non-invasive medical diagnostics systems, cutting-edge military and defense research has established conceptual similarities in these areas. Now civilian enterprises can use government innovations to facilitate optimal functionality of complex real-time systems. Advanced Signal Processing details a cost-efficient generic processing structure that exploits these commonalities to benefit commercial applications. Learn from a Renowned Defense Scientist, Researcher, and Innovator The author preserves the mathematical focus and key information from the first edition that provided invaluable coverage of topics including adaptive systems, advanced beamformers, and volume visualization methods in medicine. Integrating the best features of non-linear and conventional algorithms and explaining their application in PC-based architectures, this text contains new data on: Advances in biometrics, image segmentation, registration, and fusion techniques for 3D/4D ultrasound, CT, and MRI Fully digital 3D/ (4D: 3D+time) ultrasound system technology, computing architecture requirements, and relevant implementation issues State-of-the-art non-invasive medical procedures, non-destructive 3D tomography imaging and biometrics, and monitoring of vital signs Cardiac motion correction in multi-slice X-ray CT imaging Space-time adaptive processing and detection of targets interference-intense backgrounds comprised of clutter and jamming With its detailed explanation of adaptive, synthetic-aperture, and fusion-processing schemes with near-instantaneous convergence in 2-D and 3-D sensors (including planar, circular, cylindrical, and spherical arrays), the quality and illustration of this text’s concepts and techniques will make it a favored reference.

Signals, Systems, Transforms, and Digital Signal Processing with MATLAB® has as its principal objective simplification without compromise of rigor. Graphics, called by the author, "the language of scientists and engineers", physical interpretation of subtle mathematical concepts, and a gradual transition from basic to more advanced topics are meant to be among the important contributions of this book. After illustrating the analysis of a function through a step-by-step addition of harmonics, the book deals with Fourier and Laplace transforms. It then covers discrete time signals and systems, the z-transform, continuous- and discrete-time filters, active and passive filters, lattice filters, and continuous- and discrete-time state space models. The author goes on to discuss the Fourier transform of sequences, the discrete Fourier transform, and the fast Fourier transform, followed by Fourier-, Laplace, and z-related transforms, including Walsh–Hadamard, generalized Walsh, Hilbert, discrete cosine, Hartley, Hankel, Mellin, fractional Fourier, and wavelet. He also surveys the architecture and design of digital signal processors, computer architecture, logic design of sequential circuits, and random signals. He concludes with simplifying and demystifying the vital subject of distribution theory. Drawing on much of the author’s own research work, this book expands the domains of existence of the most important transforms and thus opens the door to a new world of applications using novel, powerful mathematical tools.

"Provides rigorous treatment of deterministic and random signals"--